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UNIVAQ RANDOM TALKS 5

Thursday June 18th 11:00 a.m. - ZOOM Videoconference platform

Prof. Arturo Kohatsu-Higa

Department of Mathematical Sciences Ritsumeikan University

UPPER BOUNDS FOR THE JOINT DENSITY OF A STABLE PROCESS AND ITS MAXIMUM

Abstract: In this article, we obtain integration by parts formulas for the joint law of a stable process and its maximum. The argument is based on a multi-level representation for the joint law which uses the theory of convex majorants for stable processes and the Chambers-Mallows-Stuck representation for stable random variables. As applications, we obtain regularity results for the joint law and upper bounds for the density and its space derivatives.

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