在深入研究经典分枝过程的基础上,进行模型的扩展与创新,进而推出随机环境中乘积受控分枝过程模型,探讨了序列log Wn的矩的存在性,且给出了相关证明,其中Wn=Zn/Pn,Pn为规范化序列,Zn为随机环境中乘积受控分枝过程。Based on the researc...在深入研究经典分枝过程的基础上,进行模型的扩展与创新,进而推出随机环境中乘积受控分枝过程模型,探讨了序列log Wn的矩的存在性,且给出了相关证明,其中Wn=Zn/Pn,Pn为规范化序列,Zn为随机环境中乘积受控分枝过程。Based on the research of classical branching processes, the model is extended and innovated, leading to a multiplicative controlled branching process in a random environment. Moreover, we explore the existence of moments of the sequence log Wn, and relevant proofs are given, where Wn=Zn/Pn, Pnis the normalized sequence, Znis the multiplicative controlled branching process in a random environment.展开更多
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。L...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.展开更多
文摘在深入研究经典分枝过程的基础上,进行模型的扩展与创新,进而推出随机环境中乘积受控分枝过程模型,探讨了序列log Wn的矩的存在性,且给出了相关证明,其中Wn=Zn/Pn,Pn为规范化序列,Zn为随机环境中乘积受控分枝过程。Based on the research of classical branching processes, the model is extended and innovated, leading to a multiplicative controlled branching process in a random environment. Moreover, we explore the existence of moments of the sequence log Wn, and relevant proofs are given, where Wn=Zn/Pn, Pnis the normalized sequence, Znis the multiplicative controlled branching process in a random environment.
文摘令{ 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.
