On homogenization of space-time dependent and degenerate random flows II

Abstract

We study the long time behavior (homogenization) of a diffusion in random medium with time and space dependent coefficients. The diffusion coefficient may degenerate. In Stochastic Process. Appl. (2007) (to appear), an invariance principle is proved for the critical rescaling of the diffusion. Here, we generalize this approach to diffusions whose space-time scaling differs from the critical one.Comment: Published in at http://dx.doi.org/10.1214/07-AIHP135 the Annales de l'Institut Henri Poincar\'e - Probabilit\'es et Statistiques (http://www.imstat.org/aihp/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quenched Invariance Principle for a Reflecting Diffusion in a Continuum Percolation Cluster

“…For the diffusion process, there are many homogenization results. In [31] and [32], annealed invariance principles were shown. (precisely, slightly stronger results were proved but not quenched results.)…”