Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 16 (2011), paper no. 38, 423-434.
Convex minorants of random walks and Lévy processes
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.
Electron. Commun. Probab. Volume 16 (2011), paper no. 38, 423-434.
Accepted: 19 August 2011
First available in Project Euclid: 7 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60G51: Processes with independent increments; Lévy processes
This work is licensed under a Creative Commons Attribution 3.0 License.
Abramson, Josh; Pitman, Jim; Ross, Nathan; Uribe Bravo, Geronimo. Convex minorants of random walks and Lévy processes. Electron. Commun. Probab. 16 (2011), paper no. 38, 423--434. doi:10.1214/ECP.v16-1648. https://projecteuclid.org/euclid.ecp/1465261994