Cut Points and Diffusions in Random Environment

Details Cut Points and Diffusions in Random Environment Cut Points and Diffusions in Random Environment

2008-05-07

arxiv.org/abs/0805.0886v1

Journal of Theoretical Probability (2009) 22: 891-933

Mathematics

Probability

44 pages; accepted for publication in "Journal of Theoretical Probability"

Scientific paper

10.1007/s10959-008-0169-3

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], 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.

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