Annealed tail estimates for a Brownian motion in a drifted Brownian potential
Probability
2007-05-23 v1
Abstract
We study Brownian motion in a drifted Brownian potential in the subexponential regime. We prove that the annealed probability of deviating below the almost sure speed has a polynomial rate of decay and compute the exponent in this power law. This provides a continuous-time analogue of what Dembo, Peres and Zeitouni proved for the transient random walk in random environment. Our method takes a completely different route, making use of Lamperti's representation together with an iteration scheme.
Keywords
Cite
@article{arxiv.math/0601500,
title = {Annealed tail estimates for a Brownian motion in a drifted Brownian potential},
author = {Marina Talet},
journal= {arXiv preprint arXiv:math/0601500},
year = {2007}
}
Comments
35 pages