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

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

2010-10-18

arxiv.org/abs/1010.3603v2

Electron. Commun. Probab., 16, no. 8, 84-95, 2011

Mathematics

Probability

12 pages

Scientific paper

10.1214/ECP.v16-1601

We study the density of the supremum of a strictly stable L\'evy 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 A.
Kuznetsov (2010) "On extrema of stable processes" are in fact absolutely
convergent series representations for the density of the supremum.

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