Extinction times of an inhomogeneous Feller diffusion process: A PDE approach

被引：4
|
作者：
Lavigne, Florian [1 ,2 ,3 ]
Roques, Lionel [1 ]
机构：
[1] INRAE, BioSP, F-84914 Avignon, France
[2] Aix Marseille Univ, I2M, Cent Marseille, CNRS, Marseille, France
[3] CNRS, ISEM UMR 5554, F-34095 Montpellier, France
来源：
EXPOSITIONES MATHEMATICAE | 2021年 / 39卷 / 01期
关键词：
Partial differential equations; Birth-death process; Extinction times; Population dynamics; Evolutionary dynamics;
D O I：
10.1016/j.exmath.2019.12.002
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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. (C) 2020 Published by ElsevierGmbH.
引用
收藏
页码：137 / 142
页数：6
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