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SUMMARY:Tal Orenshtein (WIAS\, TU-Berlin)
DTSTART:20210519T160000Z
DTEND:20210519T170000Z
DTSTAMP:20260423T004547Z
UID:PSA/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PSA/8/">Roug
 h walks in random environment</a>\nby Tal Orenshtein (WIAS\, TU-Berlin) as
  part of Probability and Stochastic Analysis at Tecnico Lisboa\n\n\nAbstra
 ct\nRandom walks in random environment (RWRE) have been extensively studie
 d in the last half-century. Functional central limit theorems (FCLT) hold 
 in some prototypical classes such the reversible and the ballistic ones. T
 he latter are treated using rather different techniques\; Kipnis-Varadhan'
 s theory for additive functionals of Markov processes is applicable in the
  reversible case whereas the main feature exploited in the ballistic class
  is a regeneration structure. Rough path theory is a deterministic theory 
 which extends classical notions of integration to singular integrators in 
 a continuous manner. It typically provides a framework for pathwise soluti
 ons of ordinary and partial stochastic differential equations driven by a 
 singular noise. In the talk we shall discuss FCLT for additive functionals
  of Markov processes and regenerative processes lifted to the rough path s
 pace. The limiting rough path has two levels. The first one is the Brownia
 n motion\, whereas in the second we see a new feature: it is the iterated 
 integral of the Brownian motion perturbed by a deterministic linear functi
 on called the area anomaly. The aforementioned classes of RWRE are covered
  as special cases. The results provide sharper information on the limiting
  path. In addition\, the construction of new examples for SDE approximatio
 ns is an immediate application.\n\nBased on collaborations (some still in 
 progress) with Johannes Bäumler\, Noam Berger\, Jean-Dominique Deuschel\,
  Olga Lopusanschi\, Nicolas Perkowski and Martin Slowik.\n\nReferences:\n\
 n1) Additive functionals as rough paths\, with Jean-Dominique Deuschel and
  Nicolas Perkowski\, Ann. Probab. 49(3): 1450-1479 (May 2021). DOI: 10.121
 4/20-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: 10.30757/ALEA
 .v18-34.\n\n3) Rough invariance principle for delayed regenerative process
 es\, arXiv:2101.05222.\n
LOCATION:https://researchseminars.org/talk/PSA/8/
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