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Pré-Publication, Document De Travail Année : 2017

Perpetual integrals convergence and extinctions in population dynamics

Résumé

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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Dates et versions

hal-01514977 , version 1 (26-04-2017)
hal-01514977 , version 2 (04-01-2019)

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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-01514977v1⟩
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