On the existence of an invariant measure for isotropic diffusions in random environment.

The results of this paper build upon those first obtained by Sznitman and Zeitouni (Invent Math 164(3), 455-567, 2006). We establish, for spacial dimensions $$d\ge 3$$ , the existence of a unique invariant measure for isotropic diffusions in random environment on $$\mathbb {R}^d$$ 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. [ABSTRACT FROM AUTHOR]