A Slow Transient Diffusion in a Drifted Stable Potential

Arvind Singh ()
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Arvind Singh: Université Pierre et Marie Curie

Journal of Theoretical Probability, 2007, vol. 20, issue 2, 153-166

Abstract: We consider a diffusion process X in a random potential $${\mathbb{V}}$$ of the form $${\mathbb{V}_x = \mathbb{S}_x -\delta x}$$ , where $$\delta$$ is a positive drift and $$\mathbb{S}$$ is a strictly stable process of index $$\alpha\in (1,2)$$ with positive jumps. Then the diffusion is transient and $$X_t / \log^\alpha t$$ converges in law towards an exponential distribution. This behaviour contrasts with the case where $${\mathbb{V}}$$ 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.

Keywords: Diffusion with random potential; stable processes; 60K37; 60J60; 60F05 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0056-3

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