Extinction and coming down from infinity of CB-processes with competition in a Lévy environment - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2018

Extinction and coming down from infinity of CB-processes with competition in a Lévy environment

Hélène Leman

Résumé

In this note, we are interested on the event of extinction and the property of coming down from infinity of continuous state branching (or CB for short) processes with competition in a Lévy environment. In particular we prove, under the so-called Grey’s condition together with the assumption that the Lévy environment does not drift towards infinity, that for any starting point the process becomes extinct in finite time a.s. Moreover if we replace the condition on the Lévy environment by an integrability condition on the competition mechanism, then the expectation of the extinction time is finite. Finally, if we assume that the competition mechanism is convex and that the jump structure associated to the environment possesses some positive exponential positive moments then we deduce that the process comes down from infinity.
Fichier principal
Vignette du fichier
paper.pdf (267.01 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01694581 , version 1 (27-01-2018)
hal-01694581 , version 2 (05-11-2018)
hal-01694581 , version 3 (04-10-2019)

Identifiants

  • HAL Id : hal-01694581 , version 2

Citer

Hélène Leman, Juan Carlos Pardo Millan. Extinction and coming down from infinity of CB-processes with competition in a Lévy environment. 2018. ⟨hal-01694581v2⟩
97 Consultations
65 Téléchargements

Partager

Gmail Facebook X LinkedIn More