Rough walks in random environments.

Resumen:   We shall discuss functional CLTs for additive functionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels of which the first one is a Brownian motion with a well-known covariance matrix. However, in the second level we see a new feature: it is the iterated integral of the same Brownian motion perturbed by a deterministic linear function called the area anomaly and characterized in terms of the model. With that one obtains sharper information on the limiting path. The construction of new examples for SDE approximations is an immediate application. Two prototypical classes of random walks in random environments are covered as special cases: the ballistic class and the random conductance model, both with respect to the annealed law. For the random conductance model we shall present a more delicate treatment which yields a quenched result under additional restrictions.

Date: Dec 01, 2021 at 16:15:00 h
Venue: Modalidad Vía Online
Speaker: Tal Orenshtein
Affiliation: TU, Berlin
Coordinator: Avelio Sepúlveda
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Posted on Nov 29, 2021 in Seminario de Probabilidades de Chile, Seminars