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2011 Functional Limit Theorems for Lévy Processes Satisfying Cramér's Condition
Matyas Barczy, Jean Bertoin
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Electron. J. Probab. 16: 2020-2038 (2011). DOI: 10.1214/EJP.v16-930

Abstract

We consider a Lévy process that starts from $x<0$ and conditioned on having a positive maximum. When Cramér's condition holds, we provide two weak limit theorems as $x$ goes to $-\infty$ for the law of the (two-sided) path shifted at the first instant when it enters $(0,\infty)$, respectively shifted at the instant when its overall maximum is reached. The comparison of these two asymptotic results yields some interesting identities related to time-reversal, insurance risk, and self-similar Markov processes.

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Matyas Barczy. Jean Bertoin. "Functional Limit Theorems for Lévy Processes Satisfying Cramér's Condition." Electron. J. Probab. 16 2020 - 2038, 2011. https://doi.org/10.1214/EJP.v16-930

Information

Accepted: 31 October 2011; Published: 2011
First available in Project Euclid: 1 June 2016

zbMATH: 1244.60049
MathSciNet: MR2851054
Digital Object Identifier: 10.1214/EJP.v16-930

Subjects:
Primary: 60G51
Secondary: 60B10, 60G18

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Vol.16 • 2011
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