| Galton-Watson Branching process is used to describe the process of biologicalreproduction, this process have been widely used in the field of populationreproduction ,particle fission ,the spread of epidemic diseases.A lot of results in theG-W process is already completed, but the corresponding results in many processwhich derivatived from the G-W process can not be proved, so it needs us to discussand research deeply to get the more deep and precise results.This paper research document [52] for further in-depth, obtained some necessaryand sufficient conditions about extinction in random environment and varyingenvironment branching process. Due to the research of random environmentbranching process has a lot of contacts with the study of random environment ofrandom sequence limit theorem, this article also research the random environment ofrandom sequence limit theorem. First of all we get the random environment of strongdeviation theorems, which basically using the interval division method that Liu wen,Yang WeiGuo have proposed in [12]. The research of strong large number law aboutrandom environment of symmetrical random variables sequence basically use the wayof classic independent distribution variables sequence studying methods-the truncatedmethod.Weighted branching process is a relatively new branching process. In this model weassume everyone has a random weight, this weight is obtained by the product of themother weight and the random factors of the particle. The random factor is a infinitedimension random vector. The model is a promotion of general branching processmodel. Weighted branching process can be used to the recursive structure, fastrecursion algorithm and multiplicative cascades. But so far relevant papers of themodel is less than other model. A lot of important issues such as extinction problems,convergence, the limitation of moment are for fully resolved. In chapter 5, we getsome conditions about extinction in certain assumption. |
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