关于随机环境中下临界分枝过程灭绝时均值的界

Bounds on the Mean of the Extinction Time of A Subcritical Branching Processes in Random Environment

在经典分枝过程的基础上研究了随机环境中的分枝过程,运用泰勒定理、中值定理得出了随机环境中下临界分枝过程的灭绝时均值的界,对分枝过程的发展有重要作用。并且在二项分布繁衍概率母函数的两状态独立同分布随机环境情况下,对灭绝时均值的界的确定给出了一个算例。

Based on the GW branching processes, this paper studies the branching processes in random environment. Bounds on the mean of the extinction time of a subcritical branching processes in random environment which has an important effect on the development of the branch- ing processes was found through Taloy theory and median theory . For the special case of the binomial probability generating function in the two state and independent identical distribution random environment ,an example was given to show how to bound the mean of the extinction time.