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

@article{Pitman2010TheGC,
title={The greatest convex minorant of Brownian motion, meander, and bridge},
author={Jim Pitman and Nathan Ross},
journal={Probability Theory and Related Fields},
year={2010},
volume={153},
pages={771-807}
}
• Published 12 November 2010
• Mathematics
• Probability Theory and Related Fields
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…
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