The maximum of a random walk reflected at a general barrier

• 成果类型: Article
• 署名作者: Hansen, NR
• 署名单位: University of Copenhagen
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000610
• 发表日期: 2006
• 页码: 15-29
• 关键词: sequence alignments; VALUES

摘要

We define the reflection of a random walk at a general barrier and derive, in case the increments are light tailed and have negative mean, a necessary and sufficient criterion for the global maximum of the reflected process to be finite a.s. If it is finite a.s., we show that the tail of the distribution of the global maximum decays exponentially fast and derive the precise rate of decay. Finally, we discuss an example from structural biology that motivated the interest in the reflection at a general barrier.