On ballistic diffusions in random environment

Abstract

In this article we investigate diffusions in random environment. We provide a sufficient condition for a strong law of large numbers with non-vanishing limiting velocity and a functional central limit theorem. In the course of this work we introduce certain regeneration times and obtain a renewal structure. As an illustration, we apply our results to a class of anisotropic gradient-type diffusions in random environment, where the technique of the environment viewed from the particle does not apply well.