The Research On The Bisexual Branching Processes In Random Environments

The bisexual branching process in random environment is a new subject that has been studied by many scholars in recent years.Now it has been involved in many fie Ids such as family surname,animal reproduction,population growth and so on.In this paper,we study the limits of the amphoteric branching process in the random enviro nment and the extinction problem.This article is divided into four chapters.Chapter One is the introduction.Firstly,the model of the bisexual galton-watson branching process in random and bisexual galton-watson branching process with popula tion-size-dependent mating and the related theoretical knowledge are introduced.Then,the development process of the bisexual galton-watson branching process in random an d bisexual galton-watson branching process with population-size-dependent mating is described.Secondly,it will present some outstanding achievements in the development of the bisexual galton-watson branching process in random and bisexual galton-watso branching process with population-size-dependent mating.Finally,the main results of t his paper are given description.In the second chapter,In this chapter,The sufficient condition and necessary cond ition for L2-convergence of normalized process {(?)} is mainly studied,In addition,t he necessary and sufficient conditions for the L1-convergence in the form of the loga rithm criterion are also given.The third chapter first introduces the random monotonicity of bisexual galton-wats on branching process in random,and then gives the bisexual galton-watson branching process in random of the pairing function which can be added.The process is a new sufficient condition with the of probability one extinction.The chapter four concludes the conclusion that bisexual galton-wstson branching p rocess with population-size-dependent mating in random La-converges to non-degenera te variables under normalized conditions.