Stability of the overshoot for Levy processes

• 成果类型: Article
• 署名作者: Doney, RA; Maller, RA
• 署名单位: University of Manchester; University of Western Australia
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2002
• 页码: 188-212
• 关键词: random-walks; EXIT

摘要

We give equivalences for conditions like X (T (r))/r -->1 and X (T*(r))/ r --> 1, where the convergence is in probability or almost sure, both as r --> 0 and r --> infinity, where X is a Levy process and T(r) and T*(r) are the first exit times of X out of the strip {(t, y) : t > 0,\y\ < r} and half-plane {(t, y) : t > 0, y less than or equal to r}, respectively. We also show, using a result of Kesten, that X(T*(r))/r --> 1 a.s. as r --> 0 is equivalent to X creeping across a level.