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Homogenization of stochastic processes in degenerate random environments via Moser’s iteration

  • Alberto Chiarini (Aix-Marseille Université)
A3 01 (Sophus-Lie room)

Abstract

We study a symmetric diffusion in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. We prove a quenched invariance principle and a quenched local central limit theorem for such a diffusion, under some moment conditions on the environment; the key tools are a local maximal inequality and a local parabolic Harnack inequality obtained with Moser’s iteration technique. As a further application of Moser’s iteration scheme, we study a continuous-time random walk on the lattice in an environment of time-dependent random conductances. We assume that the law of the conductances is ergodic with respect to space-time shifts. Also in this case, we prove a quenched invariance principle under some moment conditions on the environment.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher