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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465261964

Digital Object Identifier
doi:10.1214/ECP.v16-1601

Mathematical Reviews number (MathSciNet)
MR2763530

Zentralblatt MATH identifier
1231.60040

Subjects
Primary: 60G52: Stable processes

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

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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