Limiting behavior of a diffusion in an asymptotically stable environment

Citations of this article
Mendeley users who have this article in their library.
Get full text


Let V be a two sided random walk and let X denote a real valued diffusion process with generator frac(1, 2) eV[x]frac(d, d x) (e- V[x]frac(d, d x)). This process is the continuous equivalent of the one-dimensional random walk in random environment with potential V. Hu and Shi (1997) described the Lévy classes of X in the case where V behaves approximately like a Brownian motion. In this paper, based on some fine results on the fluctuations of random walks and stable processes, we obtain an accurate image of the almost sure limiting behavior of X when V behaves asymptotically like a stable process. These results also apply for the corresponding random walk in random environment. © 2006 Elsevier SAS. All rights reserved.




Singh, A. (2007). Limiting behavior of a diffusion in an asymptotically stable environment. Annales de l’institut Henri Poincare (B) Probability and Statistics, 43(1), 101–138.

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free