The convex minorant of a L\'{e}vy process
Probability
2012-07-31 v3
Abstract
We offer a unified approach to the theory of convex minorants of L\'{e}vy processes with continuous distributions. New results include simple explicit constructions of the convex minorant of a L\'{e}vy process on both finite and infinite time intervals, and of a Poisson point process of excursions above the convex minorant up to an independent exponential time. The Poisson-Dirichlet distribution of parameter 1 is shown to be the universal law of ranked lengths of excursions of a L\'{e}vy process with continuous distributions above its convex minorant on the interval .
Keywords
Cite
@article{arxiv.1011.3069,
title = {The convex minorant of a L\'{e}vy process},
author = {Jim Pitman and Gerónimo Uribe Bravo},
journal= {arXiv preprint arXiv:1011.3069},
year = {2012}
}
Comments
Published in at http://dx.doi.org/10.1214/11-AOP658 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)