Perpetual integrals convergence and extinctions in population dynamics

Camille Coron; Sylvie Méléard; Denis Villemonais

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arXiv · 1704.08199

Perpetual integrals convergence and extinctions in population dynamics

Camille Coron·Sylvie Méléard·Denis Villemonais

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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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Camille Coron, Sylvie Méléard, Denis Villemonais. 2017-04-26. Perpetual integrals convergence and extinctions in population dynamics. https://arxiv.org/abs/1704.08199

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