Rates of convergence of a transient diffusion in a spectrally negative levy potential

• 成果类型: Article
• 署名作者: Singh, Arvind
• 署名单位: Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000123
• 发表日期: 2008
• 页码: 279-318
• 关键词: brownian-motion; LIMIT-THEOREMS

摘要

We consider a diffusion process X in a random Levy potential V which is a solution of the informal stochastic differential equation {dX(t) = d beta(t)-1/2V '(X-t)dt, X-0 = 0, (beta B. M. independent of V). We study the rate of convergence when the diffusion is transient under the assumption that the Levy process V does not possess positive jumps. We generalize the previous results of Hu-Shi-Yor for drifted Brownian potentials. In particular, we prove a conjecture of Carmona: provided that there exists 0 < K < 1 such that E[e(kVi)] = 1, then X-t/t(k) converges to some nondegenerate distribution. These results are in a way analogous to those obtained by Kesten-Kozlov-Spitzer for the transient random walk in a random environment.