随机环境中加权分枝过程的偏差不等式  

Deviation Inequality for a Weighted Branching Process in a Random Environment

作　　者：鲁展 彭聪 邓琳 LU Zhan;PENG Cong;DENG Lin(College of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《湖北文理学院学报》2023年第11期5-7,共3页Journal of Hubei University of Arts and Science

摘　　要：令{Y_(n),n≥0}表示独立同分布随机环境ξ=(ξ_(n))n≥0中的加权分枝过程,它是一种描述个体数量随着时间变化而随机变化的随机过程,是随机环境分枝过程的一个推广。文章通过对统计量log Y_(n)0+n Y_(n)0进行研究,利用log Y_(n)的分解式和Bernstein不等式,建立随机环境加权分枝过程的一个偏差不等式。Set{Y_(n),n≥0}represents a weighted branching process in independent and identically distribute random environmentξ=(ξ_(n))n≥0,which is a random process describing the random variation of the number of individuals over time and is a generalization of the random environment branching process.This paper studies the estimator log Y_(n)0+n Y_(n)0,and by using the decomposition of log Y_(n)and Bernstein’s inequality,establishes a deviation inequality for the weighted branching process in a random environment.This result provides theoretical support for research on genetic evolution,disease transmission,population growth,and other application fields in random environments.

关 键 词：随机环境 加权分枝过程 BERNSTEIN不等式 偏差不等式 

分 类 号：O211.6[理学—概率论与数理统计]