Probability Theory and Related Fields

, Volume 153, Issue 3–4, pp 771–807 | Cite as

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

Article

Abstract

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.

Keywords

Brownian motion Path decompositions Convex minorant 

Mathematics Subject Classification (2000)

60J65 60J05 60E99 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.University of California, BerkeleyBerkeleyUSA

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