Convex minorants of random walks and Lévy processes

DOI10.1214/ECP.v16-1648zbMath1243.60039arXiv1102.0818OpenAlexW1973953219MaRDI QIDQ428673

Josh Abramson, Gerónimo Uribe Bravo, Nathan Ross, Jim W. Pitman

Publication date: 22 June 2012

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.0818

zbMATH Keywords

Lévy processesrandom walksBrownian meanderconvex minorantfluctuation theory abstract this article provides an overview of recent work on descriptions and properties of the convex minorant of random walks and Lévy processes as detailed in [uniform stickbreaking

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Sums of independent random variables; random walks (60G50)

Related Items (12)

Markovian structure in the concave majorant of Brownian motion ⋮ Conic intrinsic volumes of Weyl chambers ⋮ Convex hulls of multidimensional random walks ⋮ Asymptotic shape of the concave majorant of a Lévy process ⋮ How long is the convex minorant of a one-dimensional random walk? ⋮ The convex minorant of a Lévy process ⋮ Lipschitz minorants of Brownian motion and Lévy processes ⋮ Dini derivatives and regularity for exchangeable increment processes ⋮ Convex minorants and the fluctuation theory of L\'evy processes ⋮ Zeros of random tropical polynomials, random polygons and stick-breaking ⋮ Distribution-free properties of isotonic regression ⋮ Limit theorems for local times and applications to SDEs with jumps

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