A slow transient diffusion in a drifted stable potential

2006/12/08 by Arvind Singh, Singh, Arvind
Mathematics · #60F05 #60J60 #60K37 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F05 #msc:60J60 #msc:60K37

paper · pdf · doi:10.48550/arxiv.math/0612220

arxiv created 2006/12/08 · arxiv updated 2009/12/01

Abstract

We consider a diffusion process X in a random potential \V of the form \V_x = §_x -δx where δ is a positive drift and § is a strictly stable process of index α∈ (1,2) with positive jumps. Then the diffusion is transient and X_t / log^αt converges in law towards an exponential distribution. This behaviour contrasts with the case where \V is a drifted Brownian motion and provides an example of a transient diffusion in a random potential which is as "slow" as in the recurrent setting.

Related

• Almost sure asymptotics for a diffusion process in a drifted Brownian potential
• Annealed tail estimates for a Brownian motion in a drifted Brownian potential
• Transience, recurrence and speed of diffusions with a non-Markovian two-phase "use it or lose it" drift
• On stochastic perturbations of slowly changing dynamical systems
• Scaling limit theorems for the κ-transient random walk in random and non-random environment