The probability of exceeding a high boundary on a random time interval for a heavy-tailed random walk

• 成果类型: Article
• 署名作者: Foss, S; Palmowski, Z; Zachary, S
• 署名单位: Heriot Watt University; University of Wroclaw; Utrecht University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000269
• 发表日期: 2005
• 页码: 1936-1957
• 关键词: renewal; moments; maxima

摘要

We study the asymptotic probability that a random walk with heavy-tailed increments crosses a high boundary on a random time interval. We use new techniques to extend results of Asmussen [Ann. Appl. Probab. 8 (1998) 354-374] to completely general stopping times, uniformity of convergence over all stopping times and a wide class of nonlinear boundaries. We also give some examples and counterexamples.