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≥3 , the existence of a unique invariant measure for isotropic diffusions in random environment on Rd 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