The Study Of Limit Theorem And The Problems Related To Branching Processes In Random Environment

In this thesis, we study the limit theorems of branching processes in random environments and the related problems, the content are as follows:In the first chapter, we firstly introduce the background and development of the branching process; secondly, we give the definitions of branching processes in random environments、weighted branching processes and bisexual branching processes; Finally, we give the main results of this thesis.In the second chapter, we study the branching process in exchangeable random environment, and show that Pξ(Zn=j|Zn+k≠0) convergences in distribution to some limit.In the third chapter, we study the controlled bisexual branching processes with random controlled functions in random environments and obtain some properties of the generating function of this process.In the fourth chapter, we study the weighted branching processes and discuss the problems of the extinction problem of the weighted branching process.