The Existence Of Solution And Split-step θ Methods About Stochastic Population System

In this paper we discuss the existence and uniqueness of solution and numerical solution about stochastic population system. The thesis is divided into three parts. In the first part, the stochastic delay population dynamics driven by Levy noise is considered. Using appropriate Lyapunov functions and the Khasminskii-Mao theorem, we show that there is an unique global positive solution of the stochastic differential equations. And we also discuss asymptotic moment properties. In the second part, a class of Split-step θ methods for solving stochastic age-dependent population equations is constructed. It’s proved the numerical solution is converge to the analytical solution of the equations under the given conditions by using Holder inequality and Gronwall inequality. In the third part, based on the influence of external environment and random perturbation on stochastic population system depend ont, the stochastic age-structured population equations with dissfusion and Markovian Switching is discussed. Split-step θ methods is introduced. We proved that the numerical solution converge to the exact solution.