Quasi-stationary distributions for structured birth and death processes with mutations
| dc.creator | Collet, Pierre | |
| dc.creator | Martinez, Servet | |
| dc.creator | Méléard, Sylvie | |
| dc.creator | Martin, Jaime San | |
| dc.date | 2009-04-22 | |
| dc.date.accessioned | 2026-07-07T13:07:18Z | |
| dc.date.available | 2026-07-07T13:07:18Z | |
| dc.description | 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. | |
| dc.description | 39 pages | |
| dc.identifier | https://arxiv.org/abs/0904.3468 | |
| dc.identifier | http://arxiv.org/abs/0904.3468 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228046 | |
| dc.subject | Probability | |
| dc.subject | 92D25 (Primary); 60K35, 60J70, 60J80 (Secondary) | |
| dc.title | Quasi-stationary distributions for structured birth and death processes with mutations | |
| dc.type | text |