随机环境中带移民分枝过程的Hoeffding型不等式

Hoeffding Type Inequality for Branching Processes with Immigration in a Random Environment

考虑到自然界人口迁徙和疾病传播等现象,引入移民因素(Yn)的影响,令 {Zn,n≥0}为独立同分布环境ξ=(ξn)n≥0的一个上临界带移民分枝过程,对统计量log Zn0+n/Zn0进行研究,利用logZ_(n)的分解以及Hoeffding不等式,建立随机环境中带移民分枝过程的一个偏差不等式。

Taking into account phenomena such as population migration and the spread of diseases in the natural world,the influence of immigration factors(Yn)is introduced,let {Zn,n≥0}is a supercritical branching process with immigration in an independent and identically distributed(i.i.d.)random environmentξ=(ξn)n≥0.The paper investigates the statistic log Zn0+n/Zn0,utilizing the decomposition of logZ_(n) and Hoeffding inequality,to establish a bias inequality for the branching process with immigration in a random environment.