随机环境中加权分枝过程的概率不等式

Probability Inequalities for Weighted Branching Processes in Random Environments

令{ Yn,n≥0 }表示独立同分布随机环境ξ=(ξn)n≥0中的加权分枝过程,本文针对统计量log(Yn0+nYn0),借助Markov不等式建立了一个相关概率不等式,这一结果可以用于探索种群动态和概率特性,有助于深入理解随机环境中加权分枝模型的本质。Let { Yn,n≥0 }denote the weighted branching process in independently and identically distributed random environments ξ=(ξn)n≥0. In this paper, focusing on a statistic log(Yn0+nYn0), we establish a related probability inequality using Markov’s inequality. This result can be used to investigate population dynamics and probabilistic characteristics, contributing to a deeper understanding of the essence of weighted branching models in random environments.