Localization of favorite points for diffusion in random environment

2006/12/18 by Dimitrios Cheliotis, Cheliotis, Dimitrios · 1 citation
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #advanced mathematical theories #math.PR #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0612533

23 pages, 3 figures

arxiv created 2006/12/18 · arxiv updated 2009/12/01

Abstract

For a diffusion X_t in a one-dimensional Wiener medium W, it is known that there is a certain process b_x(W) that depends only on the environment W, so that X_t-b_logt(W) converges in distribution as t goes to infinity. We prove that, modulo a relatively small time change, the process b_x(W):x>0is followed closely by the process F_X(e^x): x>0, with F_X(t) denoting the point with the most local time for the diffusion at time t.

Cited by

• Quenched and annealed heat kernel estimates for Brox's diffusion

Related

• Localization and number of visited valleys for a transient diffusion in random environment
• Invariant distributions and scaling limits for some diffusions in time-varying random environments
• Donsker theorems for diffusions: Necessary and sufficient conditions
• The rate of decay of the Wiener sausage in local Dirichlet space
• Intrinsic Location Parameter of a Diffusion Process