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

2006/01/20 by Marina Talet, Talet, Marina
Mathematics · #60J55 #60K37 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J55 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0601500

35 pages

arxiv created 2006/01/20 · arxiv updated 2009/12/01

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.

Related

• Almost sure asymptotics for a diffusion process in a drifted Brownian potential
• The maximum of the local time of a diffusion process in a drifted Brownian potential
• A slow transient diffusion in a drifted stable potential
• An ergodic theorem for the frontier of branching Brownian motion
• Persistence exponent for random processes in Brownian scenery