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Convex minorants and the fluctuation theory of Lévy processes

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FD2W03 - Optimal control and fractional dynamics

We establish a novel characterisation of the law of the convex minorant of any Lévy process. Our self-contained elementary proof is based on the analysis of piecewise linear convex functions and requires only very basic properties of Lévy processes. Our main result provides a new simple and self-contained approach to the fluctuation theory of Lévy processes, circumventing local time and excursion theory. Easy corollaries include classical theorems, such as Rogozin’s regularity criterion, Spitzer’s identities and the Wiener-Hopf factorisation.

This talk is part of the Isaac Newton Institute Seminar Series series.

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