与年龄相关的具有扩散的随机种群系统数值解的收敛性

通常情况下,大多数与年龄相关的具有扩散的随机种群系统没有精确解,因此,数值逼近方法成为研究系统特性的主要工具.为此,给出了与年龄相关的具有扩散的随机种群系统的数值方法,应用随机泛函微分方程理论,根据Gronwall和Barkholder-Davis-Gundy引理,证明了系统的数值解收敛到其解析解.特别要指出的是,所得结论是通常种群系统现有结论的扩展.

Convergence of Numerical Solutions to Stochastic Age-structured Population System with Diffusion

In general, most of stochastic age-structured population system with diffusion do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to give a numerical scheme. By applying the theory of stochastic functional differential equation and using Gronwall lemma and Barkholder-Davis-Gundy lemma, the convergence of the numerical approximation solution to the true solution is proved for a class of stochastic age-dependent population dynamic system. In particular, the results are extension of the existing results for ordinary age-dependent population dynamic system.