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2011 Convex minorants of random walks and Lévy processes
Josh Abramson, Jim Pitman, Nathan Ross, Geronimo Uribe Bravo
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Electron. Commun. Probab. 16: 423-434 (2011). DOI: 10.1214/ECP.v16-1648


This article provides an overview of recent work on descriptions and properties of the Convex minorants of random walks and Lévy processes, which summarize and extend the literature on these subjects. The results surveyed include point process descriptions of the convex minorant of random walks and Lévy processes on a fixed finite interval, up to an independent exponential time, and in the infinite horizon case. These descriptions follow from the invariance of these processes under an adequate path transformation. In the case of Brownian motion, we note how further special properties of this process, including time-inversion, imply a sequential description for the convex minorant of the Brownian meander.


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Josh Abramson. Jim Pitman. Nathan Ross. Geronimo Uribe Bravo. "Convex minorants of random walks and Lévy processes." Electron. Commun. Probab. 16 423 - 434, 2011.


Accepted: 19 August 2011; Published: 2011
First available in Project Euclid: 7 June 2016

zbMATH: 1243.60039
MathSciNet: MR2831081
Digital Object Identifier: 10.1214/ECP.v16-1648

Primary: 60G50
Secondary: 60G51


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