Berry-Esseen Bounds Of Branching Models

In recent years,the branching model has been more widely used in species re-production,migration,extinction and the influence of external factors on species.It has always been one of the active and fruitful directions of stochastic process,and has far-reaching significance.This paper mainly studies the Berry-Esseen bounds of the multiplicative controlled branching,the Berry-Esseen bounds and the small value probability of the branching process with immigration in random environment,and convergence of the normalized process Wn related to the weighted branching process with immigration in random environment.This paper is divided into four chapters:The first chapter is the introduction,which summarizes the research background and significance of the multiplicative controlled branching process,the branching pro-cess with immigration in a random environment,and the weighted branching process with immigration in a random environment.The definition of weighted branching pro-cess with immigration in random environment is given for the first time.Finally,the main results of this paper are given.In the second chapter,we study the Berry-Esseen bounds of the asymptotic quasi-likelihood estimate 9 of the growth rate ? of the multiplicative controlled branching process(Zn).Using the existence of positive moments of random variable log W,the exponential speed of convergence of log Wn to log W is obtained,and the Berry-Esseen bounds of the estimate ? of the criticality parameter p is established.In the third chapter,we improve the Berry Esseen's bound results of the branching process with immigration in the random environment,and study the small probability of the process in the non-extinction case.In the fourth chapter,we obtain the a.s.convergence of the normalization process Wn related to the weighted branching process(Zn)with immigrating in a random environment.