Central Limit Theorem Of Branching Models And Related Problems

In recent years,the branching process in random environment have become a hot topic for scholars.With the development of branching processes,the study of bisexual branching processes has gradually become a hot topic.Referring to the content and method of the branching process in random environment,this article mainly studies Berry-Esseen's first-order asymptotic expansion of supercritical branching processes in a random environment and central limit theorem,Esseen's inequality,LP convergence and convergence rate of the bisexual branching processes.Its innovation fully utilizes the decomposition of female process Fn and the treatment of pairing function.This article is divided into five chapters:The first chapter introduces the research background for a branching process in a random environment and bisexual branching process.Secondly,it introduces the models and definitions and lists all the conclusions of this paper.In the second chapter,we study the Berry-Esseen's first-order expansions of super-critical branching processes in a random environment and give the first-order asymp-totic expansion for the random variable log Zn.In the third chapter,this chapter study the central limit theorem and Esseen's inequality for a bisexual branching process and studies the decomposition formula of random variable Zn-rnW.In the fourth chapter,based on the decomposition formula of random variable zn-?j=0 n-1r(?j)W and Zn-?j=0 n-1r(?j)W,We mainly study the central limit theorem and Esseen's inequality and four equivalent propositions of random variable Wn?W Lp.In the fifth chapter,we study the convergence rate of the bisexual branching process W-Wn in a varying environment under different moments.