A Special Kind Of Bisexual Galton-Watson Branching Process In Random Environment

Galton-Watson Branching process is used to describe the process of biological reproduction,this process have been widely used in many fields,such as population reproduction particle fission、the spread of epidemic diseases and so on.A lot of results in the G-W process have already been completed,but the corresponding results in many process which derivatived from the G-W process have not been proved.so it need us to discuss and research deeply to get the more deep and precise results.Bisexual Galton-Watson Branching process is an important part in the filed of Galton-Watson Branching process, it assumed that the population reproduction must complete by two individuals which have the different sex,so it breached the limitation of the G-W process in the reality problem. There are quite a lot of research about the Bisexual Galton-Watson Branching process in the domestic and abroad, through these research, many important nature in BPRE was extentioned to BGWPRE. But not all nature in BPRE can be extentioned. Because a lot of nature in BGWPRE was desided by the rule of mating. So in this paper, we consider a BGWPRE with a special mating function.The main results in this paper are expressed as follows:l,We popularize many common nature in BPRE to the BGWPRE by using the special mating function.2,We mainly research the extinction quality about the Bisexual Galton-Watson Branching process in the independent and identically distributed environment, we classified the situation of extinction and abtain the classification theorem.3,Furtherly we have researched the extinction probability about the Bisexual Galton-Watson Branching process in the stationary and ergodic environment,we have abtained the corresponding classification theorem,and do further studing about the extinction quality.