Limit Properties Of Bisexual Branching Processes

In recent years,the research on the bisexual branching processes has become a hot issue for many scholars.The theory of bisexual branching processes has been applied in many fields,such as the reproduction of living creature,the growth and decline of population and so on.In this paper,we mainly study the limit properties of the supercritical bisexual and controlled bisexual branching processes.The thesis includes three chapters.The first chapter is introduction.Firstly,The background and research status at home and abroad of the bisexual branching processes and controlled bisexual branch-ing processes are introduced;Secondly,the model and related definitions of bisexual branching processes and controlled bisexual branching processes are presented and rel-evant theoretical results that have been drawn by researchers at home and abroad are summarized;Finally,the main results obtained in this paper are given.In chapter 2,we give a brief overview of the research on the bisexual branching processes.According to different research contents,it will be divided into three part-s:the extinction problem,asymptotic,generating functions and moments.Based on this theory,the existence and the boundness of harmonic moments in the supercritical bisexual branching processes are further studied and the necessary and sufficient con-ditions for the finite moments of the harmonic moments are given,lastly,we discussed the problem of small value probability.In chapter 3,limiting behavior of a superadditive controlled bisexual branching processes is investigated,the relation and related property of the mean growth rate of mating unit between controlled bisexual branching processes and bisexual branching processes are studied,the upper and lower bound of the conditional mean value are obtained,what's more,limiting behaviors of sequences normalized by the upper and lower bound of the conditional mean value are studied and we give conditions for a.s.convergence?L1 convergence?L2 convergence.