On The Existence of an Invariant Measure for Isotropic Diffusions in Random Environment

Abstract

The results of this paper build upon those first obtained by Sznitman and Zeitouni in [11]. We establish, for spacial dimensions greater than two, the existence of a unique invariant measure for isotropic diffusions in random environment which are small perturbations of Brownian motion. Furthermore, we establish a general homogenization result for initial data which are locally measurable with respect to the coefficients.