2010/11/12 by Jim Pitman, Pitman, Jim, Nathan Ross +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR
paper · pdf · doi:10.48550/arxiv.1011.3073
36 pages, 2 figures
arxiv created 2010/11/12 · openalex publication_date 2010/11/12 · arxiv updated 2010/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the 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.