Electronic Communications in Probability

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

Friedrich Hubalek and Alexey Kuznetsov

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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.

Article information

Electron. Commun. Probab., Volume 16 (2011), paper no. 8, 84-95.

Accepted: 23 January 2011
First available in Project Euclid: 7 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G52: Stable processes

stable processes supremum Mellin transform double Gamma function Liouville numbers continued fractions

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Hubalek, Friedrich; Kuznetsov, Alexey. A convergent series representation for the density of the supremum of a stable process. Electron. Commun. Probab. 16 (2011), paper no. 8, 84--95. doi:10.1214/ECP.v16-1601. https://projecteuclid.org/euclid.ecp/1465261964

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