arXiv math/06122202006-12-08math.PR

A slow transient diffusion in a drifted stable potential

Arvind Singh

英文摘要：

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 $α\in (1,2)$ 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.

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