论文标题
一种处理随机人口动态中关键案例的方法
A method to deal with the critical case in stochastic population dynamics
论文作者
论文摘要
在众多论文中，通过实际数量的迹象研究了随机人口模型的行为，这是灭绝集合附近人口的增长率。在许多情况下，事实证明，当这种增长率为正时，从长远来看，该过程将持续存在，而如果为负，则该过程会收敛到灭绝。但是，很少处理生长速率的关键案例。本文的目的是提供一种可以在许多情况下应用的方法，以证明在关键情况下，时间平均水平以灭绝为例。给出了许多应用，用于随机微分方程和分段确定性的马尔可夫过程，建模猎物prodenter，传播或结构化种群动力学。
In numerous papers, the behaviour of stochastic population models is investigated through the sign of a real quantity which is the growth rate of the population near the extinction set. In many cases, it is proven that when this growth rate is positive, the process is persistent in the long run, while if it is negative, the process converges to extinction. However, the critical case when the growth rate is null is rarely treated. The aim of this paper is to provide a method that can be applied in many situations to prove that in the critical case, the process congerves in temporal average to extinction. A number of applications are given, for Stochastic Differential Equations and Piecewise Deterministic Markov Processes modelling prey-predator, epidemilogical or structured population dynamics.
