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
基金Supported by the Natural Science Foundation of Anhui Province(kj2013Z331)the Humanities and Social Sciences Foundation for the Youth Scholars of Ministry of Education of China(12YJCZH217)the Natural Science Foundation of Anhui Province(1308085MA03)
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.
基金Supported by NSFC of China(11171101,11171044)Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP,Hunan Normal University)(Ministry of Education of China)+4 种基金Open Fund Project of Key Research Institute of Philosophies and Social Sciences in Hunan Universities(12FEFM06)Hunan Provincial Natural Science Foundation of China(11JJ2001,13JJ6048)Research Fund for Doctoral Program of Higher Education of China(20104306110001)Planned Science and Technology Project of Hunan Province(2010fj 6036,2009fi3098)Scientific Research Fund of Hunan Provincial Education Department(12C0027,08C120,09C113,09C059)
