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

摘要: 令$\left\{Y_n,n\ge 0\right\}$ 表示独立同分布随机环境$\xi ={\left({\xi }_n\right)}_{n\ge 0}$ 中的加权分枝过程，本文针对统计量$log\left(\frac{\text{}{Y}_{n_0+n}}{Y_{n_0}}\right)$ ，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。

Abstract: Let $\left\{Y_n,n\ge 0\right\}$ denote the weighted branching process in independently and identically distributed random environments $\xi ={\left({\xi }_n\right)}_{n\ge 0}$ . In this paper, focusing on a statistic $log\left(\frac{\text{}{Y}_{n_0+n}}{Y_{n_0}}\right)$ , 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.