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

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.