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MiS Preprint
63/2008

On the equivalence of the static and dynamic point of view for diffusions in a random environment

Tom Schmitz

Abstract

We study the equivalence of the static and dynamic point of view for diffusions in a random environment in dimension one. First we prove that the static and dynamic distributions are equivalent if and only if either the speed in the law of large numbers does not vanish, or $b/a$ is a.s. the gradient of a stationary function, where $a$ and $b$ are the covariance coefficient resp. the local drift attached to the diffusion.

We moreover show that the equivalence of the static and dynamic point of view is characterized by the existence of so-called "almost linear coordinates".

Received:
Sep 25, 2008
Published:
Sep 29, 2008
MSC Codes:
60K37, 82D30
Keywords:
diffusion in random environment, environment viewed from the particle, invariant measures, almost linear coordinates

Related publications

inJournal
2009 Repository Open Access
Tom Schmitz

On the equivalence of the static and dynamic points of view for diffusions in a random environment

In: Stochastic processes and their applications, 119 (2009) 8, pp. 2501-2522