随机环境中带移民的上临界分枝过程的Berry-Esseen界

Berry-Esseen's bound for a supercritical branching process with immigration in a random environment

考虑独立同分布的随机环境中带移民的上临界分枝过程(Zn).应用(Zn)与随机环境中不带移民分枝过程的联系,以及与相应随机游动的联系,在一些适当的矩条件下,本文证明关于log Zn的中心极限定理的Berry-Esseen界.

We consider a supercritical branching process with immigration in an independent and identically distributed random environment.Based on its relations with branching processes(without immigration)in random environments and by using the associated random walks,we establish the Berry-Esseen bound in the central limit theorem for log Zn under suitable moment conditions.