Cut Points and Diffusions in Random Environment

Abstract

In this article we investigate the asymptotic behavior of a new class of multidimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen et al. (Ann. Inst. Henri Poincare 39(5):527–555, 2003) in the discrete setting providing a decoupling effect in the process. This allows us to take advantage of an ergodic structure to derive a strong law of large numbers with possibly vanishing limiting velocity and a central limit theorem under the quenched measure.