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arXiv · 1011.3069

The convex minorant of a L\'{e}vy process

Jim Pitman·Gerónimo Uribe Bravo
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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 $[0,1]$.

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BibTeXRIS

Jim Pitman, Gerónimo Uribe Bravo. 2010-11-12. The convex minorant of a L\'{e}vy process. https://doi.org/10.1214/11-aop658

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