One dimensional diffusion in an asymmetric random environment
Probability
2015-06-26 v1
Abstract
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.
Cite
@article{arxiv.math/0610057,
title = {One dimensional diffusion in an asymmetric random environment},
author = {Dimitrios Cheliotis},
journal= {arXiv preprint arXiv:math/0610057},
year = {2015}
}
Comments
14 pages. To appear in Annales de l'Institut Henri Poincare, Probability and Statistics