BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tal Orenshtein (WIAS\, TU-Berlin) DTSTART:20210519T160000Z DTEND:20210519T170000Z DTSTAMP:20260404T132230Z UID:PSA/8 DESCRIPTION:Title: Rough walks in random environment\nby Tal Orenshtein (WIAS\, TU-Ber lin) as part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\ nAbstract\nRandom walks in random environment (RWRE) have been extensively studied in the last half-century. Functional central limit theorems (FCLT ) hold in some prototypical classes such the reversible and the ballistic ones. The latter are treated using rather different techniques\; Kipnis-Va radhan's theory for additive functionals of Markov processes is applicable in the reversible case whereas the main feature exploited in the ballisti c class is a regeneration structure. Rough path theory is a deterministic theory which extends classical notions of integration to singular integrat ors in a continuous manner. It typically provides a framework for pathwise solutions of ordinary and partial stochastic differential equations drive n by a singular noise. In the talk we shall discuss FCLT for additive func tionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels. The first one is the Brownian motion\, whereas in the second we see a new feature: it is the it erated integral of the Brownian motion perturbed by a deterministic linear function called the area anomaly. The aforementioned classes of RWRE are covered as special cases. The results provide sharper information on the l imiting path. In addition\, the construction of new examples for SDE appro ximations is an immediate application.\n\nBased on collaborations (some st ill in progress) with Johannes Bäumler\, Noam Berger\, Jean-Dominique Deu schel\, Olga Lopusanschi\, Nicolas Perkowski and Martin Slowik.\n\nReferen ces:\n\n1) Additive functionals as rough paths\, with Jean-Dominique Deusc hel and Nicolas Perkowski\, Ann. Probab. 49(3): 1450-1479 (May 2021). DOI: 10.1214/20-AOP1488.\n\n2) Ballistic random walks in random environment as rough paths: convergence and area anomaly\, with Olga Lopusanschi\, ALEA \, Lat. Am. J. Probab. Math. Stat. 18\, 945–962 (April 2021) DOI: 10.307 57/ALEA.v18-34.\n\n3) Rough invariance principle for delayed regenerative processes\, arXiv:2101.05222.\n LOCATION:https://stable.researchseminars.org/talk/PSA/8/ END:VEVENT END:VCALENDAR