Study On Two Kinds Of Population Models In Random Environments

In 1969,Smith and Willkinson first began to study the branching process in a random environment.In recent years,this model has become a hot topic in the field of probability theory.In this paper,we mainly study the weighted moments of the branching process with immigration in a random environment,and the weighted mo-ments of the process of bisexual branching in the random environment.In this paper,we also use the theory of stochastic differential equation and the theory of Markov pro-cess to study the long-term behavior of a stochastic single population growth model with markov switching.This article is divided into four chapters:In the first chapter,firstly,we summarize the background and research status of the branching process with immigration in a random environment,bisexual branch-ing process and the stochastic single species population grow-th models with markov switching.Then we introduce the two kinds of random models.In the second chapter,we study the weighted moments of Wn,W*and W of the branching process with immigration in a random environment,and show a sufficient condition for the existence of the weighted moments.In the third chapter,we study the quenched weighted moment of the limit random variablethe(?)of the bisexual branching processes in a random environment and give two sufficient conditions for the existence of the quenched weighted moments.In the fourth chapter,we study the global existence,stochastic ultimate bounded-ness and asymptotic properties of the positive solution of the stochastic single species population growth models with markov switching and give the algebraic criterion which is easy to distinguish.Finally,we give an example for numerical simulation.