A convergent series representation for the density of the supremum of a stable process

Friedrich Hubalek (Vienna University of Technology)
Alexey Kuznetsov (York University)

Abstract


We study the density of the supremum of a strictly stable Levy process. We prove that for almost all values of the index $\alpha$ - except for a dense set of Lebesgue measure zero - the asymptotic series which were obtained in Kuznetsov (2010) "On extrema of stable processes" are in fact absolutely convergent series representations for the density of the supremum.

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Pages: 84-95

Publication Date: January 23, 2011

DOI: 10.1214/ECP.v16-1601

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