Quasi-stationary distributions for structured birth and death processes with mutations - Centre de mathématiques appliquées (CMAP) Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2009

Quasi-stationary distributions for structured birth and death processes with mutations

Résumé

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that the population will be extinct almost surely. Our goal is the study, in this infinite dimensional framework, of quasi-stationary distributions when the process is conditioned on non-extinction. We firstly show in this general setting, the existence of quasi-stationary distributions. This result is based on an abstract theorem proving the existence of finite eigenmeasures for some positive operators. We then consider a population with constant birth and death rates per individual and prove that there exists a unique quasi-stationary distribution with maximal exponential decay rate. The proof of uniqueness is based on an absolute continuity property with respect to a reference measure.
Fichier principal
Vignette du fichier
cmmm-versionsoumise.pdf (330.8 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00377518 , version 1 (22-04-2009)

Identifiants

Citer

Pierre Collet, Servet Martinez, Sylvie Méléard, Jaime San Martin. Quasi-stationary distributions for structured birth and death processes with mutations. 2009. ⟨hal-00377518⟩
215 Consultations
140 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More