SMALL DEVIATIONS OF GENERAL LEVY PROCESSES

• 成果类型: Article
• 署名作者: Aurzada, Frank; Dereich, Steffen
• 署名单位: Technical University of Berlin
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP457
• 发表日期: 2009
• 页码: 2066-2092
• 关键词: small ball probabilities; Metric Entropy

摘要

We study the small deviation problem logP(sup(t is an element of[0,1]) vertical bar X-t vertical bar <= epsilon), as epsilon -> 0, for general Levy processes X. The techniques enable us to determine the asymptotic rate for general real-valued Levy processes, which we demonstrate with many examples. As a particular consequence, we show that a Levy process with nonvanishing Gaussian component has the same (strong) asymptotic small deviation rate as the corresponding Brownian motion.