THE CONVEX MINORANT OF A LEVY PROCESS

• 成果类型: Article
• 署名作者: Pitman, Jim; Bravo, Geronimo Uribe
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP658
• 发表日期: 2012
• 页码: 1636-1674
• 关键词: random-walks; bridge; sums

摘要

We offer a unified approach to the theory of convex minorants of Levy processes with continuous distributions. New results include simple explicit constructions of the convex minorant of a Levy process on both finite and infinite time intervals, and of a Poisson point process of excursions above the convex minorant up to an independent exponential time. The Poisson Dirichlet distribution of parameter 1 is shown to be the universal law of ranked lengths of excursions of a Levy process with continuous distributions above its convex minorant on the interval [0, 1].