One dimensional diffusion in an asymmetric random environment

Details One dimensional diffusion in an asymmetric random environment One dimensional diffusion in an asymmetric random environment

2006-10-02

arxiv.org/abs/math/0610057v1

Mathematics

Probability

14 pages. To appear in Annales de l'Institut Henri Poincare, Probability and Statistics

Scientific paper

According to a theorem of S. Schumacher, for a diffusion X in an environment determined by a stable process that belongs to an appropriate class and has index a, it holds that X_t/(log t)^a converges in distribution, as t goes to infinity, to a random variable having an explicit description in terms of the environment. We compute the density of this random variable in the case the stable process is spectrally one-sided. This computation extends a result of H. Kesten and quantifies the bias that the asymmetry of the environment causes to the behavior of the diffusion.

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