Functional limit theorems for Lévy processes satisfying Cramér's condition - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2011

Functional limit theorems for Lévy processes satisfying Cramér's condition

Résumé

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.
Fichier principal
Vignette du fichier
Duality-second.pdf (231.15 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00588557 , version 1 (24-04-2011)

Identifiants

Citer

Matyas Barczy, Jean Bertoin. Functional limit theorems for Lévy processes satisfying Cramér's condition. 2011. ⟨hal-00588557⟩
194 Consultations
143 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More