Limiting behavior of a diffusion in an asymptotically stable environment

  • Singh A
  • 2


    Mendeley users who have this article in their library.
  • 3


    Citations of this article.


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.

Author-supplied keywords

  • Iterated logarithm law
  • Random environment
  • Stable process

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Arvind Singh

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free