Perpetual integrals convergence and extinctions in population dynamics

Abstract : In this article we use a criterion for the integrability of paths of one-dimensional diffusion processes from which we derive new insights on allelic fixation in several situations. This well known criterion involves a simple necessary and sufficient condition based on scale function and speed measure. We provide a new simple proof for this result and also obtain explicit bounds for the moments of such integrals. We also extend this criterion to non-homogeneous processes by use of Girsanov's transform. We apply our results to multi-type population dynamics: using the criterion with appropriate time changes, we characterize the behavior of proportions of each type before population extinction in different situations.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01514977
Contributeur : Denis Villemonais <>
Soumis le : mercredi 26 avril 2017 - 18:45:56
Dernière modification le : jeudi 15 juin 2017 - 09:09:17

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ExtinctionCDS2017-04-26.pdf
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  • HAL Id : hal-01514977, version 1

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Camille Coron, Sylvie Méléard, Denis Villemonais. Perpetual integrals convergence and extinctions in population dynamics. 2017. <hal-01514977>

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