Perpetual integrals convergence and extinctions in population dynamics
Probability
2017-04-27 v1
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.
Cite
@article{arxiv.1704.08199,
title = {Perpetual integrals convergence and extinctions in population dynamics},
author = {Camille Coron and Sylvie Méléard and Denis Villemonais},
journal= {arXiv preprint arXiv:1704.08199},
year = {2017}
}