The Research On Controlled Bisexual Branching Processes In Random Environment

We mainly discuss the controlled bisexual branching processes in random environment and some issues related to it. This thesis consists of three chapters.Chapter one, Introduction. Firstly, we introduce the present research status of branching processes and some promotional models of it. Then we give the model of controlled bisexual branching processes in random environment. At last, we outline the main results obtained in this study.Chapter two, Controlled bisexual branching processes with random control function in random environment. We discuss the Markov property, dual law and some properties of the probability generating functions of the process when the control function is a random variable.Chapter three, A class of controlled bisexual branching processes in random environment. When the control function ? is super-additive, we find two suitable normalization factors related with the mean growth rate of each pair unit, and then give the sufficient conditions of the a.s. convergence, the L~1 convergence and the L~2 convergence of the process{Z_n~*,n?Z~+}respectively normalized by these two normalization factors.