Harmonic Moments Of Bisexual Branching Process In A Random Environment And Its Related Problems

In recent years,the research on the bisexuality branching process has become a hot research topic for many scholars,and the theory of bisexuality branching process has been applied in many fields,such as biological reproduction,population growth and decline,etc.This paper mainly discusses the harmonic torque of branching processes in random environment sexes,large deviation,the deviation and growth problems.This paper is divided into four chapters:In chapter 1,which introduces the background and current research status of the bisexual branching process and the bisexual branching process in random environment.Secondly,the models and definitions of the bisexual branching process and the random environment branching process are introduced.Finally,the main results are given.In chapter 2,the harmonic moment of the bisexual process in random environment is studied.The existence,existence and boundedness of the conditional harmonic moment in the bisexual process in random environment are studied.In chapter 3,we study the upper and lower bounds of the deviations of log Zn,and the large deviations of log Zn,on the basis of the harmonic moment of chapter 2,and prove a tail probability theorem of the middle deviations of log Zn.In chapter 4,we studies the problem of the growth rate of bisexual branching process in random environment,when Zn to more critical situation,studies the Xn=Zbe-n?asymptotic distribution.