Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1156993 | Stochastic Processes and their Applications | 2008 | 31 Pages |
Abstract
For a diffusion XtXt in a one-dimensional Wiener medium WW, it is known that there is a certain process (br(W))r≥0(br(W))r≥0 that depends only on the environment, so that Xt−blogt(W)Xt−blogt(W) converges in distribution as t→∞t→∞. The paths of bb are step functions. Denote by FX(t)FX(t) the point with the most local time for the diffusion at time tt. We prove that, modulo a relatively small time change, the paths of the processes (br(W))r≥0(br(W))r≥0, (FX(er))r≥0(FX(er))r≥0 are close after some large rr.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Dimitris Cheliotis,