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

Abstract

We study the density of the supremum of a strictly stable Lévy 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.

12 pages

References in corpus (3)

• The law of the supremum of a stable Lévy process with no negative jumps
• On extrema of stable processes
• The asymptotic behavior of densities related to the supremum of a stable process

Cited by in corpus (4)

• Suprema of Lévy processes
• The hitting time of zero for a stable process
• First passage times for subordinate Brownian motions
• Simulating signed mixtures