The greatest convex minorant of Brownian motion, meander, and bridge

• 成果类型: Article
• 署名作者: Pitman, Jim; Ross, Nathan
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-011-0385-0
• 发表日期: 2012
• 页码: 771-807
• 关键词: 3-dimensional bessel process; concave majorant; continuity

摘要

This article contains both a point process and a sequential description of the greatest convex minorant of Brownian motion on a finite interval. We use these descriptions to provide new analysis of various features of the convex minorant such as the set of times where the Brownian motion meets its minorant. The equivalence of these descriptions is non-trivial, which leads to many interesting identities between quantities derived from our analysis. The sequential description can be viewed as a Markov chain for which we derive some fundamental properties.