Quasi-stationary distributions and diffusion models in population dynamics

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dc.creatorCattiaux, Patrick
dc.creatorCollet, Pierre
dc.creatorLambert, Amaury
dc.creatorMartinez, Servet
dc.creatorMéléard, Sylvie
dc.creatorMartin, Jaime San
dc.date2007-03-27
dc.date2009-01-26
dc.date.accessioned2026-07-07T12:34:08Z
dc.date.available2026-07-07T12:34:08Z
dc.descriptionIn this paper, we study quasi-stationarity for a large class of Kolmogorov diffusions. The main novelty here is that we allow the drift to go to $- \infty$ at the origin, and the diffusion to have an entrance boundary at $+\infty$. These diffusions arise as images, by a deterministic map, of generalized Feller diffusions, which themselves are obtained as limits of rescaled birth--death processes. Generalized Feller diffusions take nonnegative values and are absorbed at zero in finite time with probability 1. An important example is the logistic Feller diffusion. We give sufficient conditions on the drift near 0 and near $+ \infty$ for the existence of quasi-stationary distributions, as well as rate of convergence in the Yaglom limit and existence of the $Q$-process. We also show that under these conditions, there is exactly one quasi-stationary distribution, and that this distribution attracts all initial distributions under the conditional evolution, if and only if $+\infty$ is an entrance boundary. In particular this gives a sufficient condition for the uniqueness of quasi-stationary distributions. In the proofs spectral theory plays an important role on $L^2$ of the reference measure for the killed process.
dc.identifierhttps://arxiv.org/abs/math/0703781
dc.identifierhttp://arxiv.org/abs/math/0703781
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/217320
dc.subjectProbability
dc.subject92D25 (Primary), 37A30 (Secondary), 60K35, 60J60, 60J85, 60J70
dc.titleQuasi-stationary distributions and diffusion models in population dynamics
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