2020/01/03 by Dang Nguyen, Nguyen, Dang H., Édouard Strickler +2
Mathematics · Medicine · Social Sciences · #37A50 #37H15 #60J25 #60J60 #92D25 #92D30 #Evolutionary Game Theory and Cooperation #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2001.00895
openalex publication_date 2020/01/03 · openalex created_date 2022/11/11 · openalex updated_date 2026/07/28
In numerous papers, the behaviour of stochastic population models is\ninvestigated through the sign of a real quantity which is the growth rate of\nthe population near the extinction set. In many cases, it is proven that when\nthis growth rate is positive, the process is persistent in the long run, while\nif it is negative, the process converges to extinction. However, the critical\ncase when the growth rate is null is rarely treated. The aim of this paper is\nto provide a method that can be applied in many situations to prove that in the\ncritical case, the process congerves in temporal average to extinction. A\nnumber of applications are given, for Stochastic Differential Equations and\nPiecewise Deterministic Markov Processes modelling prey-predator,\nepidemilogical or structured population dynamics.\n