The convex minorant of a Lévy process

Details The convex minorant of a Lévy process The convex minorant of a Lévy process

2010-11-12

arxiv.org/abs/1011.3069v2

Mathematics

Probability

32 pages, 3 figures; incorporated referees suggestions; corrected Theorem 2 and its proof; to appear in Annals of Probability

Scientific paper

We offer a unified approach to the theory of convex minorants of L\'evy processes with continuous distributions. New results include simple and explicit constructions of the convex minorant of a L\'evy 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\'evy process with continuous distributions above its convex minorant on the interval $[0,1]$.

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