# 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 :
Type de document :
Pré-publication, Document de travail
2011
Domaine :

https://hal.archives-ouvertes.fr/hal-00588557
Contributeur : Jean Bertoin <>
Soumis le : dimanche 24 avril 2011 - 17:40:47
Dernière modification le : lundi 29 mai 2017 - 14:23:05
Document(s) archivé(s) le : lundi 25 juillet 2011 - 02:44:29

### Fichiers

Duality-second.pdf
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### Identifiants

• 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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## 216

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