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Annealed tail estimates for a Brownian motion in a drifted Brownian potential

Research paper by Marina Talet

Indexed on: 20 Jan '06Published on: 20 Jan '06Published in: Mathematics - Probability



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.