Asymptotic behavior of conditional laws and moments of α-stable random vectors, with application to upcrossing intensities

• 成果类型: Article
• 署名作者: Albin, JMP; Leadbetter, MR
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 1468-1500
• 关键词: random-variables; sample paths

摘要

We derive upper bounds for the conditional moment E{\ X \(e) \ Y = y} of a strictly alpha-stable random vector (X, Y) when alpha not equal 1 and rho less than or equal to 2 and prove weak convergence for the conditional law (X/u \ Y = u) as u --> infinity when alpha > 1. As an example of application, we derive a new result in crossing theory for ct-stable processes.