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May 2013 Suprema of Lévy processes
Mateusz Kwaśnicki, Jacek Małecki, Michał Ryznar
Ann. Probab. 41(3B): 2047-2065 (May 2013). DOI: 10.1214/11-AOP719

Abstract

In this paper we study the supremum functional $M_{t}=\sup_{0\le s\le t}X_{s}$, where $X_{t}$, $t\ge0$, is a one-dimensional Lévy process. Under very mild assumptions we provide a simple, uniform estimate of the cumulative distribution function of $M_{t}$. In the symmetric case we find an integral representation of the Laplace transform of the distribution of $M_{t}$ if the Lévy–Khintchin exponent of the process increases on $(0,\infty)$.

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Mateusz Kwaśnicki. Jacek Małecki. Michał Ryznar. "Suprema of Lévy processes." Ann. Probab. 41 (3B) 2047 - 2065, May 2013. https://doi.org/10.1214/11-AOP719

Information

Published: May 2013
First available in Project Euclid: 15 May 2013

zbMATH: 1288.60061
MathSciNet: MR3098066
Digital Object Identifier: 10.1214/11-AOP719

Subjects:
Primary: 60G51
Secondary: 60E10, 60J75

Rights: Copyright © 2013 Institute of Mathematical Statistics

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Vol.41 • No. 3B • May 2013
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