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2013 A note on the series representation for the density of the supremum of a stable process
Daniel Hackmann, Alexey Kuznetsov
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Electron. Commun. Probab. 18: 1-5 (2013). DOI: 10.1214/ECP.v18-2757

Abstract

An absolutely convergent double series representation for the density of the supremum of $\alpha$-stable Lévy process was obtained by Hubalek and Kuznetsov for almost all irrational $\alpha$. This result cannot be made stronger in the following sense: the series does not converge absolutely when $\alpha$ belongs to a certain subset of irrational numbers of Lebesgue measure zero. Our main result in this note shows that for every irrational $\alpha$ there is a way to rearrange the terms of the double series, so that it converges to the density of the supremum. We show how one can establish this stronger result by introducing a simple yet non-trivial modification in the original proof of Hubalek and Kuznetsov.

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Daniel Hackmann. Alexey Kuznetsov. "A note on the series representation for the density of the supremum of a stable process." Electron. Commun. Probab. 18 1 - 5, 2013. https://doi.org/10.1214/ECP.v18-2757

Information

Accepted: 6 June 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1323.60065
MathSciNet: MR3070908
Digital Object Identifier: 10.1214/ECP.v18-2757

Subjects:
Primary: 60G52

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