# Functional limit theorems for Lévy processes satisfying Cramér's condition

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 $x\to -\infty$ 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.
Mots-clés :
Document type :
Preprints, Working Papers, ...
2011
Domain :

https://hal.archives-ouvertes.fr/hal-00588557
Contributor : Jean Bertoin <>
Submitted on : Sunday, April 24, 2011 - 5:40:47 PM
Last modification on : Wednesday, October 12, 2016 - 1:04:50 AM
Document(s) archivé(s) le : Monday, July 25, 2011 - 2:44:29 AM

### Files

Duality-second.pdf
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### Identifiers

• HAL Id : hal-00588557, version 1
• ARXIV : 1104.4733

### Citation

Matyas Barczy, Jean Bertoin. Functional limit theorems for Lévy processes satisfying Cramér's condition. 2011. <hal-00588557>

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