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Extinction times of an inhomogeneous Feller diffusion process: A PDE approach
Expositiones Mathematicae ( IF 0.7 ) Pub Date : 2020-03-09 , DOI: 10.1016/j.exmath.2019.12.002
Florian Lavigne , Lionel Roques

We focus on the distribution of the extinction times of a population whose size N(t) follows a Feller diffusion process with inhomogeneous growth term r(t). Obtaining a precise description of the extinction times and of their dependence with respect to r(t) has important applications in adaptive biology, for understanding “evolutionary rescue” phenomena. A formula for the distribution of the extinction times has been recently obtained, through probabilistic arguments. The aim of this note is to propose a new derivation of this formula, based on the analysis of a degenerate parabolic partial differential equation.



中文翻译:

非均匀Feller扩散过程的消光时间:PDE方法

我们关注于一个人口灭绝时间的分布 ñŤ 遵循具有不均匀增长项的Feller扩散过程 [RŤ。获得灭绝时间及其对物种的依赖性的精确描述[RŤ在自适应生物学中具有重要的应用,可用于理解“进化拯救”现象。最近,通过概率论证,得出了消光时间分布的公式。本注释的目的是基于对退化的抛物型偏微分方程的分析,提出该公式的新推导。

更新日期:2020-03-09
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