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 follows a Feller diffusion process with inhomogeneous growth term . Obtaining a precise description of the extinction times and of their dependence with respect to 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 遵循具有不均匀增长项的Feller扩散过程 。获得灭绝时间及其对物种的依赖性的精确描述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。