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BEGIN:VEVENT
SUMMARY:Xin Guo (UC Berkeley)
DTSTART:20200504T150000Z
DTEND:20200504T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/1
DESCRIPTION:Title: Connecting Generative adversarial networks with Me
an Field Games\nby Xin Guo (UC Berkeley) as part of Oxford Stochastic
Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathem
atical Institute.\n\nAbstract\nGenerative Adversarial Networks (GANs) have
celebrated great empirical success\, especially in image generation and p
rocessing. Meanwhile\, Mean-Field Games (MFGs)\, as analytically feasible
approximations for N-player games\, have experienced rapid growth in theo
ry of controls. In this talk\, we will discuss a new theoretical connectio
ns between GANs and MFGs. Interpreting MFGs as GANs\, on one hand\, allows
us to devise GANs-based algorithm to solve MFGs. Interpreting GANs as MFG
s\, on the other hand\, provides a new and probabilistic foundation for GA
Ns. Moreover\, this interpretation helps establish an analytical connectio
n between GANs and Optimal Transport (OT) problems\, the connection previo
usly understood mostly from the geometric perspective. We will illustrate
by numerical examples of using GANs to solve high dimensional MFGs\, demon
strating its superior performance over existing methodology.\n\nRegistrati
on URL:\nhttps://zoom.us/meeting/register/tJ0oceGoqDsrH9PwXl9eEUDoA6rGri-Z
af_R\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Schied (University of Waterloo)
DTSTART:20200511T150000Z
DTEND:20200511T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/2
DESCRIPTION:Title: Weierstrass bridges\nby Alexander Schied (Univ
ersity of Waterloo) as part of Oxford Stochastic Analysis and Mathematical
Finance Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbst
ract\nMany classical fractal functions\, such as the Weierstrass and Takag
i-van der Waerden functions\, admit a finite p-th variation along a natura
l sequence of partitions. They can thus serve as integrators in pathwise I
tô calculus. Motivated by this observation\, we introduce a new class of
stochastic processes\, which we call Weierstrass bridges. They have contin
uous sample paths and arbitrarily low regularity and so provide a new exam
ple class of “rough” stochastic processes. We study some of their samp
le path properties including p-th variation and moduli of continuity. This
talk includes joint work with Xiyue Han and Zhenyuan Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Nourdin (University of Luxembourg)
DTSTART:20200518T150000Z
DTEND:20200518T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/3
DESCRIPTION:Title: The functional Breuer-Major theorem\nby Ivan N
ourdin (University of Luxembourg) as part of Oxford Stochastic Analysis an
d Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical Inst
itute.\n\nAbstract\nLet $X=\\{ X_n\\}_{n\\in \\mathbb{Z}}$ be zero-mean st
ationary Gaussian sequence of random variables with covariance function $\
\rho$ satisfying $\\rho(0)=1$. Let $\\varphi:\\mathbb{R}\\to\\mathbb{R}$ b
e a function such that $E[\\varphi(X_0)^2]<\\infty$ and assume that $\\var
phi$ has Hermite rank $d \\geq 1$. The celebrated Breuer-Major theorem ass
erts that\, if $\\sum_{r\\in\\mathbb{Z}} |\\rho(r)|^d<\\infty$ then the fi
nite dimensional distributions of $\\frac1{\\sqrt{n}}\\sum_{i=0}^{\\lfloor
n\\cdot\\rfloor-1} \\varphi(X_i)$ converge to those of $\\sigma\\\,W$\, w
here $W$ is a standard Brownian motion and $\\sigma$ is some (explicit) co
nstant. Surprisingly\, and despite the fact this theorem has become over t
he years a prominent tool in a bunch of different areas\, a necessary and
sufficient condition implying the weak convergence in the space ${\\bf D}(
[0\,1])$ of càdlàg functions endowed with the Skorohod topology is still
missing. Our main goal in this paper is to fill this gap. More precisely\
, by using suitable boundedness properties satisfied by the generator of t
he Ornstein-Uhlenbeck semigroup\, we show that tightness holds under the s
ufficient (and almost necessary) natural condition that $E[|\\varphi(X_0)|
^{p}]<\\infty$ for some $p>2$.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fabian Harang (Oslo)
DTSTART:20200525T150000Z
DTEND:20200525T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/4
DESCRIPTION:Title: Infinitely regularising paths and regularisation b
y noise.\nby Fabian Harang (Oslo) as part of Oxford Stochastic Analysi
s and Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical
Institute.\n\nAbstract\nWe discuss regularization by noise from a pathwise
perspective using non-linear Young integration\, and discuss the relation
s with occupation measures and local times. This methodology of pathwise r
egularization by noise was originally proposed by Gubinelli and Catellier
(2016)\, who use the concept of averaging operators and non-linear Young i
ntegration to give meaning to certain ill posed SDEs. \nIn a recent work t
ogether with Nicolas Perkowski we show that there exists a class of path
s with exceptional regularizing effects on ODEs\, using the framework of G
ubinelli and Catellier. In particular we prove existence and uniqueness of
ODEs perturbed by such a path\, even when the drift is given as a Schwart
z distribution. Moreover\, the flow associated to such ODEs are proven to
be infinitely differentiable. Our analysis can be seen as purely pathwise\
, and is only depending on the existence of a sufficiently regular occupat
ion measure associated to the path added to the ODE. As an example\, we sh
ow that a certain type of Gaussian processes has infinitely differentiable
local times\, whose paths then can be used to obtain the infinitely regul
arizing effect on ODEs. This gives insight into the powerful effect that n
oise may have on certain equations. If time permits\, I will also discuss
an ongoing extension of these results towards regularization of certain P
DE/SPDEs by noise.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frederi Viens (Michigan State University)
DTSTART:20200601T150000Z
DTEND:20200601T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/5
DESCRIPTION:Title: A martingale approach for fractional Brownian moti
ons and related path dependent PDEs\nby Frederi Viens (Michigan State
University) as part of Oxford Stochastic Analysis and Mathematical Finance
Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nWe
study dynamic backward problems\, with the computation of conditional exp
ectations as a special objective\, in a framework where the (forward) stat
e process satisfies a Volterra type SDE\, with fractional Brownian motion
as a typical example. Such processes are neither Markov processes nor semi
martingales\, and most notably\, they feature a certain time inconsistency
which makes any direct application of Markovian ideas\, such as flow prop
erties\, impossible without passing to a path-dependent framework. Our mai
n result is a functional Itô formula\, extending the Functional Ito calcu
lus to our more general framework. In particular\, unlike in the Functiona
l Ito calculus\, where one needs only to consider stopped paths\, here we
need to concatenate the observed path up to the current time with a certai
n smooth observable curve derived from the distribution of the future path
s. We then derive the path dependent PDEs for the backward problems. Fina
lly\, an application to option pricing and hedging in a financial market w
ith rough volatility is presented.\n\nJoint work with JianFeng Zhang (USC)
.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christina Goldschmidt (Oxford)
DTSTART:20200608T150000Z
DTEND:20200608T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/6
DESCRIPTION:Title: The scaling limit of a critical random directed gr
aph\nby Christina Goldschmidt (Oxford) as part of Oxford Stochastic An
alysis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathemat
ical Institute.\n\nAbstract\nWe consider the random directed graph $\\vec{
G}(n\,p)$ with vertex set $\\{1\,2\,\\ldots\,n\\}$ in which each of the $n
(n-1)$ possible directed edges is present independently with probability $
p$. We are interested in the strongly connected components of this directe
d graph. A phase transition for the emergence of a giant strongly connecte
d component is known to occur at $p = 1/n$\, with critical window $p= 1/n
+ \\lambda n^{-4/3}$ for $\\lambda \\in \\mathcal{R}$. We show that\, with
in this critical window\, the strongly connected components of $\\vec{G}(n
\,p)$\, ranked in decreasing order of size and rescaled by $n^{-1/3}$\, co
nverge in distribution to a sequence $(\\mathcal{C}_1\,\\mathcal{C}_2\,\\l
dots)$ of finite strongly connected directed multigraphs with edge lengths
which are either 3-regular or loops. The convergence occurs the sense of
an $\\ell^1$ sequence metric for which two directed multigraphs are close
if there are compatible isomorphisms between their vertex and edge sets wh
ich roughly preserve the edge-lengths. Our proofs rely on a depth-first ex
ploration of the graph which enables us to relate the strongly connected c
omponents to a particular spanning forest of the undirected Erdős-Rényi
random graph $G(n\,p)$\, whose scaling limit is well understood. We show t
hat the limiting sequence $(\\mathcal{C}_1\,\\mathcal{C}_2\,\\ldots)$ cont
ains only finitely many components which are not loops. If we ignore the e
dge lengths\, any fixed finite sequence of 3-regular strongly connected di
rected multigraphs occurs with positive probability.\n\nThis is joint work
with Robin Stephenson (Sheffield).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykhaylo Shkolnikov (Princeton)
DTSTART:20200615T150000Z
DTEND:20200615T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/7
DESCRIPTION:Title: Local stochastic volatility and the inverse of the
Markovian projection\nby Mykhaylo Shkolnikov (Princeton) as part of O
xford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held
in Oxford Mathematical Institute.\n\nAbstract\nThe calibration problem fo
r local stochastic volatility models leads to two-dimensional stochastic d
ifferential equations of McKean-Vlasov type. In these equations\, the cond
itional distribution of the second component of the solution given the fir
st enters the equation for the first component of the solution. While such
equations enjoy frequent application in the financial industry\, their ma
thematical analysis poses a major challenge. I will explain how to prove t
he strong existence of stationary solutions for these equations\, as well
as the strong uniqueness in an important special case. \nBased on joint wo
rk with Daniel Lacker and Jiacheng Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kurtz (University of Wisconsin)
DTSTART:20200622T150000Z
DTEND:20200622T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/8
DESCRIPTION:Title: Controlled and constrained martingale problems
\nby Thomas Kurtz (University of Wisconsin) as part of Oxford Stochastic A
nalysis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathema
tical Institute.\n\nAbstract\nMost of the basic results on martingale prob
lems extend to the setting in which the generator depends on a control. T
he “control” could represent a random environment\, or the generator c
ould specify a classical stochastic control problem. The equivalence betwe
en the martingale problem and forward equation (obtained by taking expecta
tions of the martingales) provides the tools for extending linear programm
ing methods introduced by Manne in the context of controlled finite Markov
chains to general Markov stochastic control problems. The controlled mar
tingale problem can also be applied to the study of constrained Markov pro
cesses (e.g.\, reflecting diffusions)\, the boundary process being treated
as a control. The talk includes joint work with Richard Stockbridge and
with Cristina Costantini.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Karatzas (Columbia University)
DTSTART:20201012T150000Z
DTEND:20201012T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/9
DESCRIPTION:Title: A trajectorial approach to the gradient flow prope
rties of conservative diffusions and Markov chains\nby Ioannis Karatza
s (Columbia University) as part of Oxford Stochastic Analysis and Mathemat
ical Finance Seminar\n\nLecture held in Oxford Mathematical Institute.\n\n
Abstract\nWe provide a detailed\, probabilistic interpretation for the var
iational characterization of conservative diffusion as entropic gradient f
low. Jordan\, Kinderlehrer\, and Otto showed in 1998 that\, for diffusions
of Langevin-Smoluchowski type\, the Fokker-Planck probability density flo
w minimizes the rate of relative entropy dissipation\, as measured by the
distance traveled in terms of the quadratic Wasserstein metric in the ambi
ent space of configurations. Using a very direct perturbation analysis we
obtain novel\, stochastic-process versions of such features\; these are va
lid along almost every trajectory of the motion in both the forward and\,
most transparently\, the backward\, directions of time. The original resul
ts follow then simply by “aggregating”\, i.e.\, taking expectations. A
s a bonus\, the HWI inequality of Otto and Villani relating relative entro
py\, Fisher information\, and Wasserstein distance\, falls in our lap\; an
d with it the celebrated log-Sobolev\, Talagrand and Poincare inequalities
of functional analysis. Similar ideas work in the context of continuous-t
ime Markov Chains\; but now both the functional analysis and the geometry
are considerably more involved.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Steve Shreve (Carnegie Mellon University)
DTSTART:20201026T160000Z
DTEND:20201026T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/10
DESCRIPTION:Title: Diffusion Limit of Poisson Limit-Order Book Model
s\nby Steve Shreve (Carnegie Mellon University) as part of Oxford Stoc
hastic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford
Mathematical Institute.\n\nAbstract\nTrading of financial instruments has
largely moved away from floor trading and onto electronic exchanges. Ord
ers to buy and sell are queued at these exchanges in a limit-order book. W
hile a full analysis of the dynamics of a limit-order book requires an und
erstanding of strategic play among multiple agents\, and is thus extremely
complex\, so-called zero-intelligence Poisson models have been shown to c
apture many of the statistical features of limit-order book evolution. Th
ese models can be addressed by traditional queueing theory techniques\, in
cluding Laplace transform analysis. In this work\, we demonstrate in a si
mple setting that another queueing theory technique\, approximating the Po
isson model by a diffusion model identified as the limit of a sequence of
scaled Poisson models\, can also be implemented. We identify the diffusio
n limit\, find an embedded semi-Markov model in the limit\, and determine
the statistics of the embedded semi-Markov model. Along the way\, we intro
duce and study a new type of process\, a generalization of skew Brownian m
otion that we call two-speed Brownian motion.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christa Cuchiero (University of Vienna)
DTSTART:20201019T150000Z
DTEND:20201019T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/11
DESCRIPTION:Title: Deep neural networks\, generic universal interpol
ation and controlled ODEs\nby Christa Cuchiero (University of Vienna)
as part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\n
Lecture held in Oxford Mathematical Institute.\n\nAbstract\nA recent parad
igm views deep neural networks as discretizations of certain controlled or
dinary differential equations\, sometimes called neural ordinary different
ial equations. We make use of this perspective to link expressiveness of d
eep networks to the notion of controllability of dynamical systems. Using
this connection\, we study an expressiveness property that we call univers
al interpolation\, and show that it is generic in a certain sense. The uni
versal interpolation property is slightly weaker than universal approximat
ion\, and disentangles supervised learning on finite training sets from ge
neralization properties. We also show that universal interpolation holds f
or certain deep neural networks even if large numbers of parameters are le
ft untrained\, and are instead chosen randomly. This lends theoretical sup
port to the observation that training with random initialization can be su
ccessful even when most parameters are largely unchanged through the train
ing. Our results also explore what a minimal amount of trainable parameter
s in neural ordinary differential equations could be without giving up on
expressiveness.\n\nJoint work with Martin Larsson\, Josef Teichmann.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julien Dubedat (Columbia University)
DTSTART:20201102T160000Z
DTEND:20201102T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/12
DESCRIPTION:Title: Stochastic Ricci Flow on surfaces\nby Julien
Dubedat (Columbia University) as part of Oxford Stochastic Analysis and Ma
thematical Finance Seminar\n\nLecture held in Oxford Mathematical Institut
e.\n\nAbstract\nThe Ricci flow on a surface is an intrinsic evolution of t
he metric converging to a constant curvature metric within the conformal c
lass. It can be seen as an (infinite-dimensional) gradient flow. We introd
uce a natural 'Langevin' version of this flow\, thus constructing an SPDE
with invariant measure expressed in terms of Liouville Conformal Field The
ory.\n\nJoint work with Hao Shen (Wisconsin).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Massimiliano Gubinelli (Bonn)
DTSTART:20201116T160000Z
DTEND:20201116T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/13
DESCRIPTION:Title: Elliptic stochastic quantisation and supersymmetr
y\nby Massimiliano Gubinelli (Bonn) as part of Oxford Stochastic Analy
sis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathematica
l Institute.\n\nAbstract\nStochastic quantisation is\, broadly speaking\,
the use of a stochastic differential equation to construct a given probabi
lity distribution. Usually this refers to Markovian Langevin evolution wit
h given invariant measure. However we will show that it is possible to con
struct other kind of equations (elliptic stochastic partial differential e
quations) whose solutions have prescribed marginals. This connection was d
iscovered in the '80 by Parisi and Sourlas in the context of dimensional r
eduction of statistical field theories in random external fields. This pur
ely probabilistic results has a proof which depends on a supersymmetric fo
rmulation of the problem\, i.e. a formulation involving a non-commutative
random field defined on a non-commutative space. \nThis talk is based on j
oint work with S. Albeverio and F. C. de Vecchi.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Beatrice Acciaio (ETH Zurich)
DTSTART:20201130T160000Z
DTEND:20201130T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/14
DESCRIPTION:Title: Model-independence in a fixed-income market and w
eak optimal transport\nby Beatrice Acciaio (ETH Zurich) as part of Oxf
ord Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held i
n Oxford Mathematical Institute.\n\nAbstract\nI consider model-independen
t pricing problems in a stochastic interest rates framework. In this case
the usual tools from Optimal Transport and Skorokhod embedding cannot be a
pplied. I will show how some pricing problems in a fixed-income market can
be reformulated as Weak Optimal Transport (WOT) problems as introduced by
Gozlan et al. I will present a super-replication theorem that follows fro
m an extension of WOT results to the case of non-convex cost functions.\n\
nThis talk is based on joint work with M. Beiglboeck and G. Pammer.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:RenYuan Xu (University of Oxford)
DTSTART:20201123T160000Z
DTEND:20201123T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/15
DESCRIPTION:Title: Excursion risk\nby RenYuan Xu (University of
Oxford) as part of Oxford Stochastic Analysis and Mathematical Finance Sem
inar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nThe ri
sk and return profiles of a broad class of dynamic trading strategies\, in
cluding pairs trading and other statistical arbitrage strategies\, may be
characterized in terms of excursions of the market price of a portfolio aw
ay from a reference level. We propose a mathematical framework for the ris
k analysis of such strategies\, based on a description in terms of price e
xcursions\, first in a pathwise setting\, without probabilistic assumption
s\, then in a Markovian setting.\n\nWe introduce the notion of δ-excursio
n\, defined as a path which deviates by δ from a reference level before r
eturning to this level. We show that every continuous path has a unique de
composition into δ-excursions\, which is useful for scenario analysis of
dynamic trading strategies\, leading to simple expressions for the number
of trades\, realized profit\, maximum loss and drawdown. As δ is decrease
d to zero\, properties of this decomposition relate to the local time of t
he path.\n\nWhen the underlying asset follows a Markov process\, we combin
e these results with Ito's excursion theory to obtain a tractable decompos
ition of the process as a concatenation of independent δ-excursions\, who
se distribution is described in terms of Ito's excursion measure. We provi
de analytical results for linear diffusions and give new examples of stoch
astic processes for flexible and tractable modeling of excursions. Finally
\, we describe a non-parametric scenario simulation method for generating
paths whose excursion properties match those observed in empirical data.\n
\nJoint work with Anna Ananova and Rama Cont.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diyora Salimova (ETH Zurich)
DTSTART:20201109T160000Z
DTEND:20201109T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/16
DESCRIPTION:Title: Space-time deep neural network approximations for
high-dimensional partial differential equations\nby Diyora Salimova (
ETH Zurich) as part of Oxford Stochastic Analysis and Mathematical Finance
Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nIt
is one of the most challenging issues in applied mathematics to approxima
tely solve high-dimensional partial differential equations (PDEs) and most
of the numerical approximation methods for PDEs in the scientific literat
ure suffer from the so-called curse of dimensionality (CoD) in the sense t
hat the number of computational operations employed in the corresponding a
pproximation scheme to obtain an approximation precision 𝜀>0 grows exp
onentially in the PDE dimension and/or the reciprocal of 𝜀. Recently\,
certain deep learning based approximation methods for PDEs have been propo
sed and various numerical simulations for such methods suggest that deep
neural network (DNN) approximations might have the capacity to indeed over
come the CoD in the sense that the number of real parameters used to desc
ribe the approximating DNNs grows at most polynomially in both the PDE di
mension 𝑑∈\n and the reciprocal of the prescribed approximation accur
acy 𝜀>0. There are now also a few rigorous mathematical results in the
scientific literature which substantiate this conjecture by proving that
DNNs overcome the CoD in approximating solutions of PDEs. Each of these
results establishes that DNNs overcome the CoD in approximating suitable P
DE solutions at a fixed time point 𝑇>0 and on a compact cube [𝑎\,
𝑏]𝑑 but none of these results provides an answer to the question whe
ther the entire PDE solution on [0\,𝑇]×[𝑎\,𝑏]𝑑 can be approxi
mated by DNNs without the CoD. \nIn this talk we show that for every 𝑎
∈\\R\, 𝑏∈(𝑎\,∞) solutions of suitable Kolmogorov PDEs can be
approximated by DNNs on the space-time region [0\,𝑇]×[𝑎\,𝑏]𝑑
without the CoD.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrick Cheridito (ETH Zurich)
DTSTART:20201207T160000Z
DTEND:20201207T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/17
DESCRIPTION:Title: Efficient approximation of high-dimensional funct
ions with neural networks\nby Patrick Cheridito (ETH Zurich) as part o
f Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture h
eld in Oxford Mathematical Institute.\n\nAbstract\nWe develop a framework
for showing that neural networks can overcome the curse of dimensionality
in different high-dimensional approximation problems. Our approach is base
d on the notion of a catalog network\, which is a generalization of a stan
dard neural network in which the nonlinear activation functions can vary f
rom layer to layer as long as they are chosen from a predefined catalog of
functions. As such\, catalog networks constitute a rich family of continu
ous functions. We show that under appropriate conditions on the catalog\,
catalog networks can efficiently be approximated with ReLU-type networks a
nd provide precise estimates on the number of parameters needed for a give
n approximation accuracy. As special cases of the general results\, we obt
ain different classes of functions that can be approximated with ReLU netw
orks without the curse of dimensionality.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donghan Kim (Columbia University)
DTSTART:20210125T160000Z
DTEND:20210125T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/18
DESCRIPTION:Title: Open Markets\nby Donghan Kim (Columbia Univer
sity) as part of Oxford Stochastic Analysis and Mathematical Finance Semin
ar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nAn open
market is a subset of a larger equity market\, composed of a certain fixed
number of top‐capitalization stocks. Though the number of stocks in the
open market is fixed\, their composition changes over time\, as each comp
any's rank by market capitalization fluctuates. When one is allowed to inv
est also in a money market\, an open market resembles the entire “closed
” equity market in the sense that the market viability (lack of arbitrag
e) is equivalent to the existence of a numéraire portfolio (which cannot
be outperformed). When access to the money market is prohibited\, the clas
s of portfolios shrinks significantly in open markets\; in such a setting\
, we discuss how to construct functionally generated stock portfolios and
the concept of the universal portfolio.\nThis talk is based on joint work
with Ioannis Karatzas.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mathieu Lauriere (Princeton)
DTSTART:20210118T160000Z
DTEND:20210118T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/19
DESCRIPTION:Title: Machine Learning for Mean Field Games\nby Mat
hieu Lauriere (Princeton) as part of Oxford Stochastic Analysis and Mathem
atical Finance Seminar\n\nLecture held in Oxford Mathematical Institute.\n
\nAbstract\nMean field games (MFG) and mean field control problems (MFC) a
re frameworks to study Nash equilibria or social optima in games with a co
ntinuum of agents. These problems can be used to approximate competitive o
r cooperative situations with a large finite number of agents. They have f
ound a broad range of applications\, from economics to crowd motion\, ener
gy production and risk management. Scalable numerical methods are a key st
ep towards concrete applications. In this talk\, we propose several numeri
cal methods for MFG and MFC. These methods are based on machine learning t
ools such as function approximation via neural networks and stochastic opt
imization. We provide numerical results and we investigate the numerical a
nalysis of these methods by proving bounds on the approximation scheme. If
time permits\, we will also discuss model-free methods based on extension
s of the traditional reinforcement learning setting to the mean-field regi
me.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Titus Lupu (Sorbonne Universite)
DTSTART:20210201T160000Z
DTEND:20210201T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/20
DESCRIPTION:Title: Extremal distance and conformal radius of a $CLE_
4$ loop.\nby Titus Lupu (Sorbonne Universite) as part of Oxford Stocha
stic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford M
athematical Institute.\n\nAbstract\nThe $CLE_4$ Conformal Loop Ensemble in
a 2D simply connected domain is a random countable collection of fractal
Jordan curves that satisfies a statistical conformal invariance and appear
s\, or is conjectured to appear\, as a scaling limit of interfaces in vari
ous statistical physics models in 2D\, for instance in the double dimer mo
del. The $CLE_4$ is also related to the 2D Gaussian free field. Given a
simply connected domain D and a point z in D\, we consider the $CLE_4$ loo
p that surrounds z and study the extremal distance between the loop and th
e boundary of the domain\, and the conformal radius of the interior surrou
nded by the loop seen from z. Because of the conformal invariance\, the jo
int law of this two quantities does not depend (up to a scale factor) on t
he choice of the domain D and the point z in D. The law of the conformal r
adius alone has been known since the works of Schramm\, Sheffield and Wils
on. We complement their result by deriving the joint law of (extremal dist
ance\, conformal radius). Both quantities can be read on the same 1D Brown
ian path\, by tacking a last passage time and a first hitting time. This j
oint law\, together with some distortion bounds\, provides some exponents
related to the $CLE_4$. \n\nThis is joint work with Juhan Aru and Avelio
Sepulveda.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Del Moral (INRIA (France))
DTSTART:20210308T160000Z
DTEND:20210308T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/21
DESCRIPTION:Title: A backward Ito-Ventzell formula with an applicati
on to stochastic interpolation\nby Pierre Del Moral (INRIA (France)) a
s part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nL
ecture held in Oxford Mathematical Institute.\n\nAbstract\nWe discuss a no
vel backward Ito-Ventzell formula and an extension of the Aleeksev-Gröbne
r interpolating formula to stochastic flows. We also present some natural
spectral conditions that yield direct and simple proofs of time uniform es
timates of the difference between the two stochastic flows when their drif
t and diffusion functions are not the same\, yielding what seems to be the
first results of this type for this class of anticipative models.\n\nWe
illustrate the impact of these results in the context of diffusion perturb
ation theory\, interacting diffusions and discrete time approximations.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefano Olla (Paris Dauphine)
DTSTART:20210215T160000Z
DTEND:20210215T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/22
DESCRIPTION:Title: Thermal boundaries for energy superdiffusion\
nby Stefano Olla (Paris Dauphine) as part of Oxford Stochastic Analysis an
d Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical Inst
itute.\n\nAbstract\nhttps://www.maths.ox.ac.uk/node/38174\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Larsson (Carnegie Mellon)
DTSTART:20210208T160000Z
DTEND:20210208T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/24
DESCRIPTION:Title: Finance and Statistics: Trading Analogies for Seq
uential Learning\nby Martin Larsson (Carnegie Mellon) as part of Oxfor
d Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held in
Oxford Mathematical Institute.\n\nAbstract\nThe goal of sequential learnin
g is to draw inference from data that is gathered gradually through time.
This is a typical situation in many applications\, including finance. A se
quential inference procedure is `anytime-valid’ if the decision to stop
or continue an experiment can depend on anything that has been observed so
far\, without compromising statistical error guarantees. A recent approac
h to anytime-valid inference views a test statistic as a bet against the n
ull hypothesis. These bets are constrained to be supermartingales - hence
unprofitable - under the null\, but designed to be profitable under the re
levant alternative hypotheses. This perspective opens the door to tools fr
om financial mathematics. In this talk I will discuss how notions such as
supermartingale measures\, log-optimality\, and the optional decomposition
theorem shed new light on anytime-valid sequential learning. \n\nThis tal
k is based on joint work with Wouter Koolen (CWI)\, Aaditya Ramdas (CMU) a
nd Johannes Ruf (LSE).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Röckner (Bielefeld)
DTSTART:20210301T160000Z
DTEND:20210301T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/25
DESCRIPTION:Title: Nonlinear Fokker-Planck equations with measures a
s initial data and McKean-Vlasov equations\nby Michael Röckner (Bi
elefeld) as part of Oxford Stochastic Analysis and Mathematical Finance Se
minar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nThis
talk is about joint work with Viorel Barbu. We consider a class of nonline
ar Fokker-Planck (- Kolmogorov) equations of type \n∂𝑡𝑢(𝑡\,𝑥
)−Δ𝑥𝛽(𝑢(𝑡\,𝑥))+div(𝐷(𝑥)𝑏(𝑢(𝑡\,𝑥))𝑢(
𝑡\,𝑥))=0\,𝑢(0\,⋅)=𝜇\,\nwhere (𝑡\,𝑥)∈[0\,∞)×ℝ
𝑑\, 𝑑≥3 and 𝜇 is a signed Borel measure on ℝ𝑑 of bounded v
ariation. In the first part of the talk we shall explain how to construct
a solution to the above PDE based on classical nonlinear operator semigrou
p theory on 𝐿1(ℝ𝑑) and new results on 𝐿1−𝐿∞ regularizati
on of the solution semigroups in our case. In the second part of the talk
we shall present a general result about the correspondence of nonlinear Fo
kker-Planck equations (FPEs) and McKean-Vlasov type SDEs. In particular\,
it is shown that if one can solve the nonlinear FPE\, then one can always
construct a weak solution to the corresponding McKean-Vlasov SDE. We would
like to emphasize that this\, in particular\, applies to the singular cas
e\, where the coefficients depend "Nemytski-type" on the time-marginal law
of the solution process\, hence the coefficients are not continuous in th
e measure-variable with respect to the weak topology on probability measur
es. This is in contrast to the literature in which the latter is standardl
y assumed. Hence we can cover nonlinear FPEs as the ones above\, which are
PDEs for the marginal law densities\, realizing an old vision of McKean.\
n\nReferences V. Barbu\, M. Röckner: From nonlinear Fokker-Planck equatio
ns to solutions of distribution dependent SDE\, Ann. Prob. 48 (2020)\, no.
4\, 1902-1920. V. Barbu\, M. Röckner: Solutions for nonlinear Fokker-Pla
nck equations with measures as initial data and McKean-Vlasov equations\,
J. Funct. Anal. 280 (2021)\, no. 7\, 108926.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Bouchard (Paris Dauphine)
DTSTART:20210315T160000Z
DTEND:20210315T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/26
DESCRIPTION:Title: Ito formula for C1 functionals and path-dependent
applications in mathematical finance\nby Bruno Bouchard (Paris Dauphi
ne) as part of Oxford Stochastic Analysis and Mathematical Finance Seminar
\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nWe will di
scuss several versions of Ito’s formula in the case where the function i
s path dependent and only concave or C1 in the sense of Dupire. In particu
lar\, we will show that it can be used to solve (super) hedging problems\,
in the context of market impact or under volatility uncertainty.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Fehrman (Oxford)
DTSTART:20210222T160000Z
DTEND:20210222T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/27
DESCRIPTION:Title: Non equilibrium fluctuations in interactive parti
cle systems and conservative Stochastic PDEs\nby Benjamin Fehrman (Oxf
ord) as part of Oxford Stochastic Analysis and Mathematical Finance Semina
r\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nInteracti
ng particle systems have found diverse applications in mathematics and sev
eral related fields\, including statistical physics\, population dynamics\
, and machine learning. We will focus\, in particular\, on the zero range
process and the symmetric simple exclusion process. The large-scale beha
vior of these systems is essentially deterministic\, and is described in t
erms of a hydrodynamic limit. However\, the particle process does exhibit
large fluctuations away from its mean. Such deviations\, though rare\, c
an have significant consequences---such as a concentration of energy or th
e appearance of a vacuum---which make them important to understand and sim
ulate.\n\nIn this talk\, which is based on joint work with Benjamin Gess\,
I will introduce a continuum model for simulating rare events in the zero
range and symmetric simple exclusion process. The model is based on an a
pproximating sequence of stochastic partial differential equations with no
nlinear\, conservative noise. The solutions capture to first-order the ce
ntral limit fluctuations of the particle system\, and they correctly simul
ate rare events in terms of a large deviations principle.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davar Khoshnevisan (University of Utah)
DTSTART:20210524T150000Z
DTEND:20210524T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/28
DESCRIPTION:Title: Phase Analysis for a family of stochastic reactio
n-diffusion equations\nby Davar Khoshnevisan (University of Utah) as p
art of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLect
ure held in Oxford Mathematical Institute.\n\nAbstract\nWe consider a reac
tion-diffusion equation of the type\n∂tψ=∂2xψ+V(ψ)+λσ(ψ)W˙on (0
\,∞)×𝕋\,\nsubject to a "nice" initial value and periodic boundary\,
where 𝕋=[−1\,1] and W˙ denotes space-time white noise. The reaction
term V:ℝ→ℝ belongs to a large family of functions that includes Fish
er--KPP nonlinearities [V(x)=x(1−x)] as well as Allen-Cahn potentials [V
(x)=x(1−x)(1+x)]\, the multiplicative nonlinearity σ:ℝ→ℝ is non r
andom and Lipschitz continuous\, and λ>0 is a non-random number that meas
ures the strength of the effect of the noise W˙.\nThe principal finding o
f this paper is that: (i) When λ is sufficiently large\, the above equati
on has a unique invariant measure\; and (ii) When λ is sufficiently small
\, the collection of all invariant measures is a non-trivial line segment\
, in particular infinite. This proves an earlier prediction of Zimmerman e
t al. (2000). Our methods also say a great deal about the structure of the
se invariant measures.\n\nThis is based on joint work with Carl Mueller (U
niv. Rochester) and Kunwoo Kim (POSTECH\, S. Korea).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Pierre Fouque (University of California Santa Barbara)
DTSTART:20210614T150000Z
DTEND:20210614T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/29
DESCRIPTION:Title: Linear-Quadratic Stochastic Differential Games on
Directed Chain Networks\nby Jean-Pierre Fouque (University of Califor
nia Santa Barbara) as part of Oxford Stochastic Analysis and Mathematical
Finance Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstr
act\nWe present linear-quadratic stochastic differential games on directed
chains inspired by the directed chain stochastic differential equations i
ntroduced by Detering\, Fouque\, and Ichiba in a previous work. We solve e
xplicitly for Nash equilibria with a finite number of players and we study
more general finite-player games with a mixture of both directed chain in
teraction and mean field interaction. We investigate and compare the corre
sponding games in the limit when the number of players tends to infinity.
\nThe limit is characterized by Catalan functions and the dynamics under e
quilibrium is an infinite-dimensional Gaussian process described by a Cata
lan Markov chain\, with or without the presence of mean field interaction.
\n\nJoint work with Yichen Feng and Tomoyuki Ichiba.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thaleia Zariphopoulou (University of Texas\, Austin)
DTSTART:20210426T150000Z
DTEND:20210426T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/30
DESCRIPTION:Title: Human-machine interaction models and robo-advisin
g\nby Thaleia Zariphopoulou (University of Texas\, Austin) as part of
Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture hel
d in Oxford Mathematical Institute.\n\nAbstract\nI will introduce a family
of human-machine interaction (HMI) models in optimal portfolio constructi
on (robo-advising). Modeling difficulties stem from the limited ability to
quantify the human’s risk preferences and describe their evolution\, bu
t also from the fact that the stochastic environment\, in which the machin
e optimizes\, adapts to real-time incoming information that is exogenous t
o the human. Furthermore\, the human’s risk preferences and the machine
’s states may evolve at different scales. This interaction creates an ad
aptive cooperative game with both asymmetric and incomplete information ex
change between the two parties.\n\nAs a result\, challenging questions ari
se on\, among others\, how frequently the two parties should communicate\,
what information can the machine accurately detect\, infer and predict\,
how the human reacts to exogenous events\, how to improve the inter-linked
reliability between the human and the machine\, and others. Such HMI mode
ls give rise to new\, non-standard optimization problems that combine adap
tive stochastic control\, stochastic differential games\, optimal stopping
\, multi-scales and learning.\n\nhttps://zoom.us/meeting/register/tJEudOys
qDktEtRY1O1qvMurCmzAEkP0c91V\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fraydoun Rezakhanlou (University of California\, Berkeley)
DTSTART:20210517T150000Z
DTEND:20210517T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/31
DESCRIPTION:Title: Kinetic Theory for Hamilton-Jacobi PDEs\nby F
raydoun Rezakhanlou (University of California\, Berkeley) as part of Oxfor
d Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held in
Oxford Mathematical Institute.\n\nAbstract\nThe flow of a Hamilton-Jacobi
PDE yields a dynamical system on the space of continuous functions. When t
he Hamiltonian function is convex in the momentum variable\, and the spati
al dimension is one\, we may restrict the flow to piecewise smooth functio
ns and give a kinetic description for the solution. We regard the location
s of jump discontinuities of the first derivative of solutions as the site
s of particles. These particles interact via collisions and coagulations.
When these particles are selected randomly according to certain Gibbs meas
ures initially\, then the law of particles remains Gibbsian at later times
\, and one can derive a Boltzmann/Smoluchowski type PDE for the evolution
of these Gibbs measures. In higher dimensions\, we assume that the Hamilt
onian function is independent of position and that the initial condition
is piecewise linear and convex. Such initial conditions can be identified
as (Laguerre) tessellations and the Hamilton-Jacobi evolution can be desc
ribed as a billiard on the set of tessellations.\n\nhttps://zoom.us/meetin
g/register/tJMtce6vrzojHd0_w6e6eOTwrgM1AL7v6GT9\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Chevyrev (University of Edinburgh)
DTSTART:20210510T150000Z
DTEND:20210510T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/32
DESCRIPTION:Title: Superdiffusive limits for deterministic fast-slow
dynamical systems\nby Ilya Chevyrev (University of Edinburgh) as part
of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture
held in Oxford Mathematical Institute.\n\nAbstract\nWe consider multidime
nsional fast-slow dynamical systems in discrete-time with random initial c
onditions but otherwise completely deterministic dynamics. The question we
will investigate is whether the slow variable converges in law to a stoch
astic process under a suitable scaling limit. We will be particularly inte
rested in the case when the limiting dynamic is superdiffusive\, i.e. it c
oincides in law with the solution of a Marcus SDE driven by a discontinuou
s stable Lévy process. Under certain assumptions\, we will show that gene
rically convergence does not hold in any Skorokhod topology but does hold
in a generalisation of the Skorokhod strong M1 topology which we define us
ing so-called path functions. Our methods are based on a combination of er
godic theory and ideas arising from (but not using) rough paths. We will f
inally show that our assumptions are satisfied for a class of intermittent
maps of Pomeau-Manneville type.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuchong Zhang (University of Toronto)
DTSTART:20210607T150000Z
DTEND:20210607T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/33
DESCRIPTION:Title: Risk-Taking Contest and its Mean Field Approximat
ion\nby Yuchong Zhang (University of Toronto) as part of Oxford Stocha
stic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford M
athematical Institute.\n\nAbstract\nIn the risk-taking model of Seel and S
track\, n players decide when to stop privately observed Brownian motions
with drift and absorption at zero. They are then ranked according to their
level of stopping and paid a rank-dependent reward. We study the optimal
reward design where a principal is interested in the average performance a
nd the performance at a given rank. While the former can be related to rew
ard inequality in the Lorenz sense\, the latter can have a surprising shap
e. Next\, I will present the mean-field version of this problem. A particu
lar feature of this game is to be tractable without necessarily being smoo
th\, which turns out to offer a cautionary tale. We show that the mean fie
ld equilibrium induces n-player ε-Nash equilibria for any continuous rewa
rd function— but not for discontinuous ones. We also analyze the quality
of the mean field design (for maximizing the median performance) when use
d as a proxy for the optimizer in the n-player game. Surprisingly\, the qu
ality deteriorates dramatically as n grows. We explain this with an asympt
otic singularity in the induced n-player equilibrium distributions.\n\nJoi
nt work with M. Nutz.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jin Ma (University of Southern California)
DTSTART:20210621T150000Z
DTEND:20210621T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/34
DESCRIPTION:Title: Set-valued Backward SDEs and Set-valued Stochasti
c Analysis\nby Jin Ma (University of Southern California) as part of O
xford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held
in Oxford Mathematical Institute.\n\nAbstract\nWe establish an analytic f
ramework for studying Set-Valued Backward Stochastic Differential Equation
s (SVBSDE for short)\, motivated largely by the current studies of dynamic
set-valued risk measures for multi-asset or network-based financial model
s. Our framework will be based on the notion of Hukuhara difference betwee
n sets\, in order to compensate the lack of “inverse” operation of the
traditional Minkowski addition\, whence the vector space structure\, in t
raditional set-valued analysis. We shall examine and establish a useful fo
undation of set-valued stochastic analysis under this algebraic framework\
, including some fundamental issues regarding Aumann-Ito integrals\, espec
ially when it is connected to the martingale representation theorem. We sh
all identify some fundamental challenges and propose some extensions of th
e existing theory that are necessary to study the SVBSDEs.\n\nThis talk is
based on the joint work with Cagın Ararat and Wenqian Wu.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Cohen (University of Oxford)
DTSTART:20211011T150000Z
DTEND:20211011T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/35
DESCRIPTION:Title: Arbitrage-free market models via neural SDEs\
nby Samuel Cohen (University of Oxford) as part of Oxford Stochastic Analy
sis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathematica
l Institute.\n\nAbstract\nModelling joint dynamics of liquid vanilla optio
ns is crucial for arbitrage-free pricing of illiquid derivatives and manag
ing risks of option trade books. This paper develops a nonparametric model
for the European options book respecting underlying financial constraints
and while being practically implementable. We derive a state space for pr
ices which are free from static (or model-independent) arbitrage and study
the inference problem where a model is learnt from discrete time series d
ata of stock and option prices. We use neural networks as function approxi
mators for the drift and diffusion of the modelled SDE system\, and impose
constraints on the neural nets such that no-arbitrage conditions are pres
erved. In particular\, we give methods to calibrate neural SDE models whic
h are guaranteed to satisfy a set of linear inequalities. We validate our
approach with numerical experiments using data generated from a Heston sto
chastic local volatility model\, and will discuss some initial results usi
ng real data.\n\nBased on joint work with Christoph Reisinger and Sheng Wa
ng\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gregorios Pavliotis (Imperial College London)
DTSTART:20211018T150000Z
DTEND:20211018T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/36
DESCRIPTION:Title: On the diffusive-mean field limit for weakly inte
racting diffusions exhibiting phase transitions\nby Gregorios Pavlioti
s (Imperial College London) as part of Oxford Stochastic Analysis and Math
ematical Finance Seminar\n\nLecture held in Oxford Mathematical Institute\
, L3.\n\nAbstract\nI will present recent results on the statistical behavi
our of a large number of weakly interacting diffusion processes evolving u
nder the influence of a periodic interaction potential. We study the combi
ned mean field and diffusive (homogenisation) limits. In particular\, we s
how that these two limits do not commute if the mean field system constrai
ned on the torus undergoes a phase transition\, i.e.\, if it admits more t
han one steady state. A typical example of such a system on the torus is g
iven by mean field plane rotator (XY\, Heisenberg\, O(2)) model. As a by-p
roduct of our main results\, we also analyse the energetic consequences of
the central limit theorem for fluctuations around the mean field limit an
d derive optimal rates of convergence in relative entropy of the Gibbs mea
sure to the (unique) limit of the mean field energy below the critical tem
perature. This is joint work with Matias Delgadino (U Texas Austin) and Ri
shabh Gvalani (MPI Leipzig).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yvain Bruned (University of Edinburgh)
DTSTART:20211101T160000Z
DTEND:20211101T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/37
DESCRIPTION:Title: Locality for singular stochastic PDEs\nby Yva
in Bruned (University of Edinburgh) as part of Oxford Stochastic Analysis
and Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical In
stitute.\n\nAbstract\nWe will present the tools of regularity structures t
o deal with singular stochastic PDEs that involve non-translation invarian
t differential operators. We describe in particular the renormalized equat
ion for a very large class of spacetime dependent renormalization schemes.
Our approach bypasses the previous approaches in the translation-invarian
t setting. \n\nThis is joint work with Ismael Bailleul.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Proemel (Mannheim)
DTSTART:20211108T160000Z
DTEND:20211108T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/38
DESCRIPTION:Title: Model-free portfolio theory: a rough path approac
h\nby David Proemel (Mannheim) as part of Oxford Stochastic Analysis a
nd Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical Ins
titute.\n\nAbstract\nClassical approaches to optimal portfolio selection p
roblems are based on probabilistic models for the asset returns or prices.
However\, by now it is well observed that the performance of optimal port
folios are highly sensitive to model misspecifications. To account for var
ious type of model risk\, robust and model-free approaches have gained mor
e and more importance in portfolio theory. Based on a rough path foundatio
n\, we develop a model-free approach to stochastic portfolio theory and Co
ver's universal portfolio. The use of rough path theory allows treating si
gnificantly more general portfolios in a model-free setting\, compared to
previous model-free approaches. Without the assumption of any underlying p
robabilistic model\, we present pathwise Master formulae analogously to
the classical ones in stochastic portfolio theory\, describing the growth
of wealth processes generated by pathwise portfolios relative to the wealt
h process of the market portfolio\, and we show that the appropriately sca
led asymptotic growth rate of Cover's universal portfolio is equal to th
e one of the best retrospectively chosen portfolio. \n\nThe talk is based
on joint work with \nAndrew Allan\, Christa Cuchiero and Chong Liu.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isao Sauzedde (University of Oxford)
DTSTART:20211025T150000Z
DTEND:20211025T160000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/39
DESCRIPTION:Title: Brownian windings\nby Isao Sauzedde (Universi
ty of Oxford) as part of Oxford Stochastic Analysis and Mathematical Finan
ce Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\n
Given a point and a loop in the plane\, one can define a relative integer
which counts how many times the curve winds around the point. We will disc
uss how this winding function\, defined for almost every points in the pla
ne\, allows to define some integrals along the loop. Then\, we will invest
igate some properties of it when the loop is Brownian.\nIn particular\, we
will explain how to recover data such as the Lévy area of the curve and
its occupation measure\, based on the values of the winding of uniformly d
istributed points on the plane.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Wiesel (Columbia University)
DTSTART:20211115T160000Z
DTEND:20211115T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/40
DESCRIPTION:Title: Measuring association with Wasserstein distances<
/a>\nby Johannes Wiesel (Columbia University) as part of Oxford Stochastic
Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathe
matical Institute.\n\nAbstract\nLet π ∈ Π(μ\, ν) be a coupling betwe
en two probability measures μ and ν on a Polish space. In this talk we p
ropose and study a class of nonparametric measures of association between
μ and ν\, which we call Wasserstein correlation coefficients. These coef
ficients are based on the Wasserstein distance between ν and the disinteg
ration of π with respect to the first coordinate. We also establish basic
statistical properties of this new class of measures: we develop a statis
tical theory for strongly consistent estimators and determine their conver
gence rate in the case of compactly supported measures μ and ν. Througho
ut our analysis we make use of the so-called adapted/bicausal Wasserstein
distance\, in particular we rely on results established in [Backhoff\, Bar
tl\, Beiglböck\, Wiesel. Estimating processes in adapted Wasserstein dist
ance. 2020]. Our approach applies to probability laws on general Polish sp
aces.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Weber (University of Bath)
DTSTART:20211122T160000Z
DTEND:20211122T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/41
DESCRIPTION:Title: Gibbs measures in infinite dimensions - new resul
ts on a classical topic\nby Hendrik Weber (University of Bath) as part
of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture
held in Oxford Mathematical Institute.\n\nAbstract\nGibbs measures on spa
ces of functions or distributions play an important role in various contex
ts in mathematical physics. They can\, for example\, be viewed as continu
ous counterparts of classical spin models such as the Ising model\, they a
re an important stepping stone in the rigorous construction of Quantum Fie
ld Theories\, and they are invariant under the \nflow of certain dispersiv
e PDEs\, permitting to develop a solution theory with random initial data\
, well below the deterministic regularity threshold. \n\nThese measures ha
ve been constructed and studied\, at least since the 60s\, but over the la
st few years there has been renewed interest\, partially due to new method
s in stochastic analysis\, including Hairer’s theory of regularity struc
tures and Gubinelli-Imkeller-Perkowski’s theory of paracontrolled distri
butions. \n\nIn this talk I will present two independent but complementary
results that can be obtained with these new techniques. I will first show
how to obtain estimates on samples from of the Euclidean $\\phi^4_3$ meas
ure\, based on SPDE methods. In the second part\, I will discuss a method
to show the emergence of phase transitions in the $\\phi^4_3$ theory.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre-Francois Rodriguez (Imperial College London)
DTSTART:20211129T160000Z
DTEND:20211129T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/42
DESCRIPTION:Title: Critical exponents for a three-dimensional percol
ation model\nby Pierre-Francois Rodriguez (Imperial College London) as
part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLe
cture held in Oxford Mathematical Institute.\n\nAbstract\nWe will report o
n recent progress regarding the near-critical behavior of certain statisti
cal physics models in dimension 3. Our results deal with the second-order
phase transition associated to two percolation problems involving the Gaus
sian free field in 3D. In one case\, they determine a unique ``fixed point
'' corresponding to the transition\, which is proved to obey one of severa
l scaling relations. Such laws are classically conjectured to hold by phys
icists on the grounds of a corresponding scaling ansatz.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Morrill (University of Oxford)
DTSTART:20220117T160000Z
DTEND:20220117T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/43
DESCRIPTION:Title: Neural rough differential equations\nby James
Morrill (University of Oxford) as part of Oxford Stochastic Analysis and
Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical Instit
ute.\n\nAbstract\nNeural controlled differential equations (CDEs) are the
continuous-time analogue of recurrent neural networks\, as Neural ODEs are
to residual networks\, and offer a memory-efficient continuous-time way t
o model functions of potentially irregular time series. Existing methods f
or computing the forward pass of a Neural CDE involve embedding the incomi
ng time series into path space\, often via interpolation\, and using evalu
ations of this path to drive the hidden state. Here\, we use rough path th
eory to extend this formulation. Instead of directly embedding into path s
pace\, we instead represent the input signal over small time intervals thr
ough its \\textit{log-signature}\, which are statistics describing how the
signal drives a CDE. This is the approach for solving \\textit{rough diff
erential equations} (RDEs)\, and correspondingly we describe our main cont
ribution as the introduction of Neural RDEs. This extension has a purpose:
by generalising the Neural CDE approach to a broader class of driving sig
nals\, we demonstrate particular advantages for tackling long time series.
In this regime\, we demonstrate efficacy on problems of length up to 17k
observations and observe significant training speed-ups\, improvements in
model performance\, and reduced memory requirements compared to existing a
pproaches.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Avi Mayorcas (Cambridge)
DTSTART:20220131T160000Z
DTEND:20220131T170000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/44
DESCRIPTION:Title: Distribution dependent SDEs driven by additive co
ntinuous and fractional Brownian noise\nby Avi Mayorcas (Cambridge) as
part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLe
cture held in Oxford Mathematical Institute.\n\nAbstract\nDistribution dep
endent equations (or McKean—Vlasov equations) have found many applicatio
ns to problems in physics\, biology\, economics\, finance and computer sci
ence. Historically\, equations with either Brownian noise or zero noise ha
ve received the most attention\; many well known results can be found in t
he monographs by A. Sznitman and F. Golse. More recently\, attention has b
een paid to distribution dependent equations driven by random continuous n
oise\, in particular the recent works by M. Coghi\, J-D. Deuschel\, P. Fri
z & M. Maurelli\, with applications to battery modelling. Furthermore\, th
e phenomenon of regularisation by noise has received new attention followi
ng the works of D. Davie and M. Gubinelli & R. Catellier using techniques
of averaging along rough trajectories. Building on these ideas I will pres
ent recent joint work with L. Galeati and F. Harang concerning well-posedn
ess and stability results for distribution dependent equations driven firs
t by merely continuous noise and secondly driven by fractional Brownian mo
tion.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clement Mouhot (Cambridge)
DTSTART:20220207T153000Z
DTEND:20220207T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/45
DESCRIPTION:Title: Quantitative Hydrodynamic Limits of Stochastic La
ttice Systems\nby Clement Mouhot (Cambridge) as part of Oxford Stochas
tic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford Ma
thematical Institute.\n\nAbstract\nI will present a simple abstract quanti
tative method for proving the hydrodynamic limit of interacting particle s
ystems on a lattice\, both in the hyperbolic and parabolic scaling. In the
latter case\, the convergence rate is uniform in time. This "consistency-
stability" approach combines a modulated Wasserstein-distance estimate com
paring the law of the stochastic process to the local Gibbs measure\, toge
ther with stability estimates à la Kruzhkov in weak distance\, and consis
tency estimates exploiting the regularity of the limit solution. It avoids
the use of “block estimates” and is self-contained. We apply it to th
e simple exclusion process\, the zero range process\, and the Ginzburg-Lan
dau process with Kawasaki dynamics. This is a joint work with Daniel Marah
rens and Angeliki Menegaki (IHES).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Crisan (Imperial College London)
DTSTART:20220228T153000Z
DTEND:20220228T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/46
DESCRIPTION:Title: A general criterion for the existence and uniquen
ess of maximal solutions for a class of Stochastic Partial Differential Eq
uations\nby Dan Crisan (Imperial College London) as part of Oxford Sto
chastic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxfor
d Mathematical Institute.\n\nAbstract\nModern atmospheric and ocean scienc
e require sophisticated geophysical fluid dynamics models. Among them\, st
ochastic partial differential equations (SPDEs) have become increasingly r
elevant. The stochasticity in such models can account for the effect of th
e unresolved scales (stochastic parametrizations)\, model uncertainty\, un
specified boundary condition\, etc. Whilst there is an extensive SPDE lite
rature\, most of it covers models with unrealistic noise terms\, making th
em un-applicable to geophysical fluid dynamics modelling. There are nevert
heless notable exceptions: a number of individual SPDEs with specific form
s and noise structure have been introduced and analysed\, each of which wi
th bespoke methodology and painstakingly hard arguments. In this talk I wi
ll present a criterion for the existence of a unique maximal strong soluti
on for nonlinear SPDEs. The work is inspired by the abstract criterion of
Kato and Lai [1984] valid for nonlinear PDEs. The criterion is designed to
fit viscous fluid dynamics models with Stochastic Advection by Lie Transp
ort (SALT) as introduced in Holm [2015]. As an immediate application\, I s
how that the incompressible SALT 3D Navier-Stokes equation on a bounded d
omain has a unique maximal solution.\n\nThis is joint work with Oana Lang\
, Daniel Goodair and Romeo Mensah and it is partially supported by Europea
n Research Council (ERC)\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:XueRong Mao (University of Strathclyde)
DTSTART:20220307T153000Z
DTEND:20220307T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/47
DESCRIPTION:Title: Positivity preserving truncated Euler-Maruyama me
thod for stochastic Lotka-Volterra model\nby XueRong Mao (University o
f Strathclyde) as part of Oxford Stochastic Analysis and Mathematical Fina
nce Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\
nMost of SDE models in epidemics\, ecology\, biology\, finance etc. are hi
ghly nonlinear and do not have explicit solutions. Monte Carlo simulations
have played a more and more important role. This talk will point out seve
ral well-known numerical schemes may fail to preserve the positivity or mo
ment of the solutions to SDE models. Reliable numerical schemes are theref
ore required to be designed so that the corresponding Monte Carlo simulati
ons can be trusted. The talk will then concentrate on new numerical scheme
s for the well-known stochastic Lotka--Volterra model for interacting mult
i-species. This model has some typical features: highly nonlinear\, positi
ve solution and multi-dimensional. The known numerical methods including t
he tamed/truncated Euler-Maruyama (EM) applied to it do not preserve its p
ositivity. The aim of this talk is to modify the truncated EM to establish
a new positive preserving truncated EM (PPTEM).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gudmund Pammer (ETH Zurich)
DTSTART:20220221T153000Z
DTEND:20220221T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/48
DESCRIPTION:Title: The Wasserstein space of stochastic processes & c
omputational aspects\nby Gudmund Pammer (ETH Zurich) as part of Oxford
Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held in O
xford Mathematical Institute.\n\nAbstract\nWasserstein distance induces a
natural Riemannian structure for the probabilities on the Euclidean space.
This insight of classical transport theory is fundamental for tremendous
applications in various fields of pure and applied mathematics. We believe
that an appropriate probabilistic variant\, the adapted Wasserstein dista
nce $AW$\, can play a similar role for the class $FP$ of filtered processe
s\, i.e. stochastic processes together with a filtration. In contrast to o
ther topologies for stochastic processes\, probabilistic operations such a
s the Doob-decomposition\, optimal stopping and stochastic control are con
tinuous w.r.t. $AW$. We also show that $(FP\, AW)$ is a geodesic space\, i
sometric to a classical Wasserstein space\, and that martingales form a cl
osed geodesically convex subspace. Finally we consider computational aspec
ts and provide a novel method based on the Sinkhorn algorithm.\nThe talk i
s based on articles with Daniel Bartl\, Mathias Beiglböck and Stephan Eck
stein.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukasz Szpruch (Alan Turing Institute)
DTSTART:20220509T143000Z
DTEND:20220509T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/49
DESCRIPTION:Title: Exploration-exploitation trade-off for continuous
-time episodic reinforcement learning with linear-convex models\nby Lu
kasz Szpruch (Alan Turing Institute) as part of Oxford Stochastic Analysis
and Mathematical Finance Seminar\n\nLecture held in Oxford Mathematical I
nstitute.\n\nAbstract\nWe develop a probabilistic framework for analysing
model-based reinforcement learning in the episodic setting. We then apply
it to study finite-time horizon stochastic control problems with linear dy
namics but unknown coefficients and convex\, but possibly irregular\, obje
ctive function. Using probabilistic representations\, we study regularity
of the associated cost functions and establish precise estimates for the p
erformance gap between applying optimal feedback control derived from esti
mated and true model parameters. We identify conditions under which this p
erformance gap is quadratic\, improving the linear performance gap in rece
nt work [X. Guo\, A. Hu\, and Y. Zhang\, arXiv preprint\, arXiv:2104.09311
\, (2021)]\, which matches the results obtained for stochastic linear-quad
ratic problems. Next\, we propose a phase-based learning algorithm for whi
ch we show how to optimise exploration-exploitation trade-off and achieve
sublinear regrets in high probability and expectation. When assumptions ne
eded for the quadratic performance gap hold\, the algorithm achieves an or
der $O(N‾‾√lnN)$ high probability regret\, in the general case\, and
an order $O((lnN)^2)$ expected regret\, in self-exploration case\, over N
episodes\, matching the best possible results from the literature. The an
alysis requires novel concentration inequalities for correlated continuous
-time observations\, which we derive.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Norris (Cambridge University)
DTSTART:20220425T143000Z
DTEND:20220425T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/50
DESCRIPTION:Title: Scaling limits for Hastings-Levitov aggregation w
ith sub-critical parameters\nby James Norris (Cambridge University) as
part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLe
cture held in Oxford Mathematical Institute.\n\nAbstract\nWe consider\, in
a framework of iterated random conformal maps\, a two-parameter aggregati
on model of Hastings-Levitov type\, in which the size and intensity of new
particles are each chosen to vary as a power of the density of harmonic m
easure. Then we consider a limit in which the overall intensity of particl
es become large\, while the particles themselves become small. For a certa
in `sub-critical' range of parameter values\, we can show a law of large n
umbers and fluctuation central limit theorem. The admissible range of para
meters includes an off-lattice version of the Eden model\, for which we ca
n show that disk-shaped clusters are stable. Many open problem remain\, no
t least because the limit PDE does not yet have a satisfactory mathematica
l theory. \nThis is joint work with Vittoria Silvestri and Amanda Turner.\
n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mouhamadou Sy (Imperial College London)
DTSTART:20220523T143000Z
DTEND:20220523T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/51
DESCRIPTION:Title: Constructing global solutions to energy supercrit
ical PDEs\nby Mouhamadou Sy (Imperial College London) as part of Oxfor
d Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held in
Oxford Mathematical Institute.\n\nAbstract\nIn this talk\, we will discuss
invariant measures techniques to establish probabilistic global well-pose
dness for PDEs. We will go over the limitations that the Gibbs measures an
d the so-called fluctuation-dissipation measures encounter in the context
of energy-supercritical PDEs. Then\, we will present a new approach combin
ing the two aforementioned methods and apply it to the energy supercritica
l Schrödinger equations. We will point out other applications as well.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thaleia Zariphopoulou (University of Texas Austin)
DTSTART:20220516T143000Z
DTEND:20220516T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/52
DESCRIPTION:Title: This seminar has been cancelled\nby Thaleia Z
ariphopoulou (University of Texas Austin) as part of Oxford Stochastic Ana
lysis and Mathematical Finance Seminar\n\nLecture held in Oxford Mathemati
cal Institute.\n\nAbstract\nI will introduce a class of mean-field games u
nder forward performance and for general risk preferences. Players interac
t through competition in fund management\, driven by relative performance
concerns in an asset diversification setting. This results in a common-noi
se mean field game. I will present the value and the optimal policies of s
uch games\, as well as some concrete examples. I will also discuss the par
tial information case\, i.e.. when the risk premium is not directly observ
ed.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Michael Leahy (Imperial College London)
DTSTART:20220613T143000Z
DTEND:20220613T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/53
DESCRIPTION:Title: Fluid dynamics on geometric rough paths and varia
tional principles\nby James Michael Leahy (Imperial College London) as
part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLe
cture held in Oxford Mathematical Institute.\n\nAbstract\nNoether’s theo
rem plays a fundamental role in modern physics by relating symmetries of a
Lagrangian to conserved quantities of the Euler-Lagrange equations. In id
eal fluid dynamics\, the theorem relates the particle labeling symmetry to
a Kelvin circulation law. Circulation is conserved for incompressible flu
ids and\, otherwise\, is generated by advected variables through the momen
tum map due to a broken symmetry. We will introduce variational principles
for fluid dynamics that constrain advection to be the sum of a smooth and
geometric rough-in-time vector field. The corresponding rough Euler-Poinc
are equations satisfy a Kelvin circulation theorem and lead to a natural f
ramework to develop parsimonious non-Markovian parameterizations of subgri
d-scale dynamics.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christa Cuchiero (University of Vienna)
DTSTART:20221128T153000Z
DTEND:20221128T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/54
DESCRIPTION:Title: Universal approximation of path space functionals
\nby Christa Cuchiero (University of Vienna) as part of Oxford Stochas
tic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford Ma
thematical Institute.\n\nAbstract\nWe introduce functional input neural n
etworks defined on infinite dimensional weighted spaces\, where we use an
additive family as hidden layer maps and a non-linear activation function
applied to each hidden layer. Relying on approximation theory based on Sto
ne-Weierstrass and Nachbin type theorems on weighted spaces\, we can prove
global universal approximation results for (differentiable and) continuou
s functions going beyond approximation on compact sets. This applies in pa
rticular to approximation of (non-anticipative) path space functionals via
functional input neural networks but also via linear maps of the signatur
e of the respective paths. We apply these results in the context of stocha
stic portfolio theory to generate path dependent portfolios that are train
ed to outperform the market portfolio. The talk is based on joint works wi
th Philipp Schmocker and Josef Teichmann.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giuseppe Cannizzaro (University of Warwick)
DTSTART:20221024T143000Z
DTEND:20221024T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/55
DESCRIPTION:Title: Edwards-Wilkinson fluctuations for the Anisotropi
c KPZ in the weak coupling regime\nby Giuseppe Cannizzaro (University
of Warwick) as part of Oxford Stochastic Analysis and Mathematical Finance
Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nWe
present recent results on an anisotropic variant of the Kardar-Parisi-Zha
ng equation\, the Anisotropic KPZ equation (AKPZ)\, in the critical spatia
l dimension d=2. This is a singular SPDE which is conjectured to capture t
he behaviour of the fluctuations of a large family of random surface growt
h phenomena but whose analysis falls outside of the scope not only of clas
sical stochastic calculus but also of the theory of Regularity Structures
and paracontrolled calculus. We first consider a regularised version of th
e AKPZ equation which preserves the invariant measure and prove the conjec
ture made in [Cannizzaro\, Erhard\, Toninelli\, "The AKPZ equation at stat
ionarity: logarithmic superdiffusivity"]\, i.e. we show that\, at large sc
ales\, the correlation length grows like t1/2 (log t)1/4 up to lower order
correction. Second\, we prove that in the so-called weak coupling regime\
, i.e. the equation regularised at scale N and the coefficient of the nonl
inearity tuned down by a factor (log N)-1/2\, the AKPZ equation converges
to a linear stochastic heat equation with renormalised coefficients. Time
allowing\, we will comment on how some of the techniques introduced can be
applied to other SPDEs and physical systems at and above criticality.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Konstantinos Dareiotis (University of Leeds)
DTSTART:20221017T143000Z
DTEND:20221017T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/56
DESCRIPTION:Title: Regularisation of differential equations by multi
plicative fractional noise\nby Konstantinos Dareiotis (University of L
eeds) as part of Oxford Stochastic Analysis and Mathematical Finance Semin
ar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nIn this
talk\, we consider differential equations perturbed by multiplicative frac
tional Brownian noise. Depending on the value of the Hurst parameter $H$\,
the resulting equation is pathwise viewed as an ordinary ($H>1$)\, Young
($H \\in (1/2\, 1)$) or rough ($H \\in (1/3\, 1/2)$) differential equati
on. In all three regimes we show regularisation by noise phenomena by prov
ing the strongest kind of well-posedness for equations with irregular dri
fts: strong existence and path-by-path uniqueness. In the Young and smooth
regime $H>1/2$ the condition on the drift coefficient is optimal in the s
ense that it agrees with the one known for the additive case.\n\nIn the ro
ugh regime $H\\in(1/3\,1/2)$ we assume positive but arbitrarily small drif
t regularity for strong \nwell-posedness\, while for distributional drift
we obtain weak existence. \nThis is a joint work with Máté Gerencsér.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laure Dumaz (Ecole Normale Superieure)
DTSTART:20221031T153000Z
DTEND:20221031T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/57
DESCRIPTION:Title: Some aspects of the Anderson Hamiltonian with whi
te noise\nby Laure Dumaz (Ecole Normale Superieure) as part of Oxford
Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held in Ox
ford Mathematical Institute.\n\nAbstract\nI will present several results o
n the Anderson Hamiltonian with white noise potential in dimension 1. This
operator formally writes « - Laplacian + white noise ». It arises as th
e scaling limit of various discrete models and its explicit potential allo
ws for a detailed description of its spectrum. We will discuss localizatio
n of its eigenfunctions as well as the behavior of the local statistics of
its eigenvalues. Around large energies\, we will see that the eigenfuncti
ons are localized and follow a universal shape given by the exponential of
a Brownian motion plus a drift\, a behavior already observed by Rifkind a
nd Virag in tridiagonal matrix models. Based on joint works with Cyril Lab
bé.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johannes Ruf (LSE)
DTSTART:20221114T153000Z
DTEND:20221114T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/58
DESCRIPTION:Title: Minimum curvature flow and martingale exit times<
/a>\nby Johannes Ruf (LSE) as part of Oxford Stochastic Analysis and Mathe
matical Finance Seminar\n\nLecture held in Oxford Mathematical Institute.\
n\nAbstract\nWhat is the largest deterministic amount of time T∗ that a\
nsuitably normalized martingale X can be kept inside a convex body K in Rd
?\nWe show\, in a viscosity framework\, that T∗ equals the time it takes
for the\nrelative boundary of K to reach X(0) as it undergoes a geometric
flow that\nwe call (positive) minimum curvature flow. This result has clo
se links to\nthe literature on stochastic and game representations of geom
etric flows.\nMoreover\, the minimum curvature flow can be viewed as an ar
rival time\nversion of the Ambrosio–Soner codimension-(d − 1) mean cur
vature flow of the\n1-skeleton of K. We present very preliminary sampling-
based numerical\napproximations to the solution of the corresponding PDE.
The numerical part\nis work in progress.\nThis work is based on a collabor
ation with Camilo Garcia Trillos\, Martin\nLarsson\, and Yufei Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eyal Neuman (Imperial College London)
DTSTART:20221010T143000Z
DTEND:20221010T153000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/59
DESCRIPTION:Title: The Effective Radius of Self Repelling Elastic Ma
nifolds\nby Eyal Neuman (Imperial College London) as part of Oxford St
ochastic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxfo
rd Mathematical Institute.\n\nAbstract\nWe study elastic manifolds with se
lf-repelling \nterms and estimate their effective radius. This class of \n
manifolds is modelled by a self-repelling vector-valued Gaussian free fiel
d \nwith Neumann boundary conditions over the domain $[-N\,N]^d\\cap \\mat
hbb{Z}^d$\, \nthat takes values in $\\mathbb{R}^D$. Our main results state
that for two \ndimensional domain and range ($D=2$ and $d=2$)\, the effec
tive radius $R_N$ of the manifold is\napproximately $N$. When the dimensio
n of the domain is $d=2$ and the dimension of the range is $D=1$\, the eff
ective radius $R_N$ of the manifold is approximately $N^{4/3}$. This verif
ies the conjecture of Kantor\, Kardar and Nelson. \n\nWe also provide resu
lts for the case where $d \\geq 3$ and $D \\leq d$\, namely we give a lowe
r bound on \n$R_N$ of order $N^{\\frac{1}{D} \\left(d-\\frac{2(d-D)}{D+2}
\\right)}$ and an \nupper bound proportional to $N^{\\frac{d}{2}+\\frac{d-
D}{D+2}}$. These results \nimply that self-repelling elastic manifolds wit
h a low dimensional range \nundergo a significantly stronger stretching th
an in the case where \nd=D. \n\nThis is a joint work with Carl Mueller.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tadahiro Oh (University of Edinburgh)
DTSTART:20221107T153000Z
DTEND:20221107T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/60
DESCRIPTION:Title: Gibbs measures\, canonical stochastic quantizatio
n and singular stochastic wave equations\nby Tadahiro Oh (University o
f Edinburgh) as part of Oxford Stochastic Analysis and Mathematical Financ
e Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nI
will discuss the (non-)construction of the focusing\nGibbs measures and t
he associated dynamical problems. This study was\ninitiated by Lebowitz\,
Rose\, and Speer (1988) and continued by Bourgain\n(1994)\, Brydges-Slade
(1996)\, and Carlen-Fröhlich-Lebowitz (2016). In\nthe one-dimensional set
ting\, we consider the mass-critical case\, where a\ncritical mass thresho
ld is given by the mass of the ground state on the\nreal line. In this cas
e\, I will show that the Gibbs measure is indeed\nnormalizable at the opti
mal mass threshold\, thus answering an open\nquestion posed by Lebowitz\,
Rose\, and Speer (1988).\n\nIn the three dimensional-setting\, I will firs
t discuss the construction\nof the $\\Phi^3_3$-measure with a cubic intera
ction potential. This\nproblem turns out to be critical\, exhibiting a pha
se transition:\nnormalizability in the weakly nonlinear regime and non-nor
malizability\nin the strongly nonlinear regime. Then\, I will discuss the
dynamical\nproblem for the canonical stochastic quantization of the\n$\\Ph
i^3_3$-measure\, namely\, the three-dimensional stochastic damped\nnonline
ar wave equation with a quadratic nonlinearity forced by an\nadditive spac
e-time white noise (= the hyperbolic $\\Phi^3_3$-model). As\nfor the local
theory\, I will describe the paracontrolled approach to\nstudy stochastic
nonlinear wave equations\, introduced in my work with\nGubinelli and Koch
(2018). In the globalization part\, I introduce a new\,\nconceptually sim
ple and straightforward approach\, where we directly work\nwith the (trunc
ated) Gibbs measure\, using the variational formula and\nideas from theory
of optimal transport.\n \n\nThe first part of the talk is based on a join
t work with Philippe Sosoe\n(Cornell) and Leonardo Tolomeo (Bonn/Edinburgh
)\, while the second part\nis based on a joint work with Mamoru Okamoto (O
saka) and Leonardo\nTolomeo (Bonn/Edinburgh).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Darrick Lee (University of Oxford)
DTSTART:20221121T153000Z
DTEND:20221121T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/61
DESCRIPTION:Title: Mapping Space Signatures\nby Darrick Lee (Uni
versity of Oxford) as part of Oxford Stochastic Analysis and Mathematical
Finance Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstr
act\nWe introduce the mapping space signature\, a generalization of the pa
th signature for maps from higher dimensional cubical domains\, which is m
otivated by the topological perspective of iterated integrals by K. T. Che
n. We show that the mapping space signature shares many of the analytic an
d algebraic properties of the path signature\; in particular it is univers
al and characteristic with respect to Jacobian equivalence classes of cubi
cal maps. \nThis is joint work with Chad Giusti\, Vidit Nanda\, and Harald
Oberhauser.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:ZhongMin Qian (University of Oxford)
DTSTART:20230206T153000Z
DTEND:20230206T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/62
DESCRIPTION:Title: Monte-Carlo simulations for wall-bounded incompre
ssible viscous fluid flows\nby ZhongMin Qian (University of Oxford) as
part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLe
cture held in Oxford Mathematical Institute.\n\nAbstract\nI will present s
everal new stochastic representations for solutions of the Navier-Stokes e
quations in a wall-bounded region\, in the spirit of mean field theory. Th
ese new representations are\nobtained by using the duality of conditional
laws associated with the Taylor diffusion family.\nBy using these represen
tation\, Monte-Carlo simulations for boundary fluid flows\, including\nbou
ndary turbulence\, may be implemented. Numerical experiments are given to
demonstrate the usefulness\nof this approach.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Patrícia Gonçalves (Pontifical Catholic University of Rio de Jan
eiro)
DTSTART:20230123T153000Z
DTEND:20230123T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/63
DESCRIPTION:Title: Particle exchange models with several conservatio
n laws\nby Patrícia Gonçalves (Pontifical Catholic University of Rio
de Janeiro) as part of Oxford Stochastic Analysis and Mathematical Financ
e Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\nI
n this talk I will present an exclusion process with different types of pa
rticles: A\, B and C. This last type can be understood as holes. Two scali
ng limits will be discussed: hydrodynamic limits in the boundary driven se
tting\; and equilibrium fluctuations for an evolution on the torus. In the
later case\, we distinguish several cases\, that depend on the choice of
the jump rates\, for which we get in the limit either the stochastic Burge
rs equation or the Ornstein-Uhlenbeck equation. These results match with p
redictions from non-linear fluctuating hydrodynamics. \n(Joint work with G
. Cannizzaro\, A. Occelli\, R. Misturini).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Bank (TU Berlin)
DTSTART:20230227T153000Z
DTEND:20230227T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/64
DESCRIPTION:Title: Trading on a noisy signal: explicit solution to a
n infinite-dimensional stochastic optimal control problem\nby Peter Ba
nk (TU Berlin) as part of Oxford Stochastic Analysis and Mathematical Fina
nce Seminar\n\nLecture held in Oxford Mathematical Institute.\n\nAbstract\
nWe consider an investor who is dynamically informed about the future evol
ution of one of the independent Brownian motions driving a stock's price f
luctuations. The resulting rough semimartingale dynamics allow for strong
arbitrage\, but with linear temporary price impact the resulting optimal i
nvestment problem with exponential utility turns out to be well posed. The
dynamically revealed Brownian path segment makes the problem infinite-dim
ensional\, but by considering its convex-analytic dual problem\, we show t
hat it still can be solved explicitly and we give some financial-economic
insights into the optimal investment strategy and the properties of maximu
m expected utility. \n(Joint work with Yan Dolinsky\, Hebrew University of
Jerusalem).\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ellen Powell (Durham)
DTSTART:20230306T153000Z
DTEND:20230306T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/65
DESCRIPTION:Title: Brownian excursions\, conformal loop ensembles an
d critical Liouville quantum gravity\nby Ellen Powell (Durham) as part
of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture
held in Oxford Mathematical Institute.\n\nAbstract\nIt was recently shown
by Aidekon and Da Silva how to construct a growth fragmentation process f
rom a planar Brownian excursion. I will explain how this same growth fragm
entation process arises in another setting: when one decorates a certain
“critical Liouville quantum gravity random surface” with a conformal l
oop ensemble of parameter 4. This talk is based on joint work with Juhan A
ru\, Nina Holden and Xin Sun.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roland Bauerschmidt (University of Cambridge)
DTSTART:20230220T153000Z
DTEND:20230220T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/66
DESCRIPTION:Title: Random forests and the OSp(1|2) nonlinear sigma m
odel\nby Roland Bauerschmidt (University of Cambridge) as part of Oxfo
rd Stochastic Analysis and Mathematical Finance Seminar\n\nLecture held in
Oxford Mathematical Institute.\n\nAbstract\nGiven a finite graph\, the ar
boreal gas is the measure on\nforests (subgraphs without cycles) in which
each edge is weighted by a\nparameter β greater than 0. Equivalently this
model is bond percolation\nconditioned to be a forest\, the independent s
ets of the graphic matroid\,\nor the q→0 limit of the random cluster rep
resentation of the q-state\nPotts model. Our results rely on the fact that
this model is also the\ngraphical representation of the nonlinear sigma m
odel with target space\nthe fermionic hyperbolic plane H^{0|2}\, whose sym
metry group is the\nsupergroup OSp(1|2).\n\nThe main question we are inter
ested in is whether the arboreal gas\npercolates\, i.e.\, whether for a gi
ven β the forest has a connected\ncomponent that includes a positive frac
tion of the total edges of the\ngraph. We show that in two dimensions a Me
rmin-Wagner theorem associated\nwith the OSp(1|2) symmetry of the nonlinea
r sigma model implies that the\narboreal gas does not percolate for any β
greater than 0. On the other\nhand\, in three and higher dimensions\, we
show that percolation occurs\nfor large β by proving that the OSp(1|2) sy
mmetry of the non-linear\nsigma model is spontaneously broken. We also sho
w that the broken\nsymmetry is accompanied by massless fluctuations (Golds
tone mode). This\nresult is achieved by a renormalisation group analysis c
ombined with\nWard identities from the internal symmetry of the sigma mode
l.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Cass (Imperial College London)
DTSTART:20230116T153000Z
DTEND:20230116T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/67
DESCRIPTION:Title: Topologies and functions on unparameterised path
space\nby Thomas Cass (Imperial College London) as part of Oxford Stoc
hastic Analysis and Mathematical Finance Seminar\n\nLecture held in Oxford
Mathematical Institute.\n\nAbstract\nThe signature is a non-commutative e
xponential that appeared in the foundational work of K-T Chen in the 1950s
. It is also a fundamental object in the theory of rough paths (Lyons\, 19
98). More recently\, it has been proposed\, and used\, as part of a practi
cal methodology to give a way of summarising multimodal\, possibly irregul
arly sampled\, time-ordered data in a way that is insensitive to its param
eterisation. A key property underpinning this approach is the ability of l
inear functionals of the signature to approximate arbitrarily any compactl
y supported and continuous function on (unparameterised) path space. We pr
esent some new results on the properties of a selection of topologies on t
he space of unparameterised paths. We discuss various applications in this
context.\nThis is based on joint work with Willliam Turner.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Luitgard Veraart (London School of Economics)
DTSTART:20230130T153000Z
DTEND:20230130T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/68
DESCRIPTION:Title: Systemic Risk in Markets with Multiple Central Co
unterparties\nby Luitgard Veraart (London School of Economics) as part
of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLecture
held in Oxford Mathematical Institute.\n\nAbstract\nAbstract: We provide
a framework for modelling risk and quantifying payment shortfalls in clear
ed markets with multiple central counterparties (CCPs). Building on the st
ylised fact that clearing membership is shared among CCPs\, we show how th
is can transmit stress across markets through multiple CCPs. We provide st
ylised examples to lay out how such stress transmission can take place\, a
s well as empirical evidence to illustrate that the mechanisms we study co
uld be relevant in practice. Furthermore\, we show how stress mitigation m
echanisms such as variation margin gains haircutting by one CCP can have s
pillover effects on other CCPs. The framework can be used to enhance CCP s
tress-testing\, which currently relies on the “Cover 2” standard requi
ring CCPs to be able to withstand the default of their two largest clearin
g members. We show that who these two clearing members are can be signific
antly affected by higher-order effects arising from interconnectedness thr
ough shared clearing membership. Looking at the full network of CCPs and s
hared clearing members is therefore important from a financial stability p
erspective.\n\nThis is joint work with Iñaki Aldasoro.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolas Tapia (Weierstrass Institute Berlin)
DTSTART:20230213T153000Z
DTEND:20230213T163000Z
DTSTAMP:20260404T111213Z
UID:OxfordStochasticAnalysis/69
DESCRIPTION:Title: Stability of deep residual neural networks via di
screte rough paths\nby Nikolas Tapia (Weierstrass Institute Berlin) as
part of Oxford Stochastic Analysis and Mathematical Finance Seminar\n\nLe
cture held in Oxford Mathematical Institute.\n\nAbstract\nUsing rough path
techniques\, we provide a priori estimates for the\noutput of Deep Residu
al Neural Networks in terms of both the input data and\nthe (trained) netw
ork weights. As trained network weights are typically very\nrough when see
n as functions of the layer\, we propose to derive stability\nbounds in te
rms of the total p-variation of trained weights for any p∈[1\,3].\nUnlik
e the C1-theory underlying the neural ODE literature\, our estimates\nrema
in bounded even in the limiting case of weights behaving like Brownian\nmo
tions\, as suggested in [Cohen-Cont-Rossier-Xu (2021) Scaling Properties o
f Deep\nResidual Networks\, http://proceedings.mlr.press/v139/cohen21b/coh
en21b.pdf ]. \nMathematically\, we interpret residual neural network as so
lutions to (rough) difference equations\, and analyse them based on recent
results of discrete time signatures and rough path theory. Based\non join
t work with C. Bayer and P. K. Friz.\n
LOCATION:https://stable.researchseminars.org/talk/OxfordStochasticAnalysis
/69/
END:VEVENT
END:VCALENDAR