Let(Z_(n))be a supercritical bisexual branching process in a random environmentξ.We study the almost sure(a.s.)convergence rate of the submartingale W_(n)=Z_(n)/In to its limit W,where(In)is an usually used norming s...Let(Z_(n))be a supercritical bisexual branching process in a random environmentξ.We study the almost sure(a.s.)convergence rate of the submartingale W_(n)=Z_(n)/In to its limit W,where(In)is an usually used norming sequence.We prove that under a moment condition of order p∈(1,2),W-W_(n)=o(e^(-na))a.s.for some a>0 that we find explicitly;assuming the logarithmic moment condition holds,we haveW-W_(n)=o(n^(-α))a.s..In order to obtain these results,we provide the L^(p)-convergence of(W_(n));similar conclusions hold for a bisexual branching process in a varying environment.展开更多
在随机环境中两性分枝过程L^1-收敛的对数判别准则的基础上,以条件均值增长率的上确界作为规范化因子,令{ε_k (ξ_n)}和{σ_k (ξ_n)}为非增长序列,当k≥k_0时,给出了W_n→WL^2的必要条件sum from k=0 to ∞ k^(-1)σ_k (ξ_n)<∞,...在随机环境中两性分枝过程L^1-收敛的对数判别准则的基础上,以条件均值增长率的上确界作为规范化因子,令{ε_k (ξ_n)}和{σ_k (ξ_n)}为非增长序列,当k≥k_0时,给出了W_n→WL^2的必要条件sum from k=0 to ∞ k^(-1)σ_k (ξ_n)<∞,同时求出了在一定条件下,当k≥1时,{W_n;n∈N}依L^2-收敛到非退化到的随机变量W的充分条件是sum from k=0 to ∞ k^(-1)σ_k (ξ_n)<∞和sum from k=0 to ∞ k^(-1)ε_k (ξ_n)<∞。展开更多
基金supported by the Fundamental Research Funds for the Central University (Grant No.19JNLH09)Innovation Team Project in Guangdong Province,P.R.China (Grant No.2016WCXTD004)+1 种基金supported by the National Natural Science Foundation of China (Grants no.11731012,12271062)Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science&Technology)。
文摘Let(Z_(n))be a supercritical bisexual branching process in a random environmentξ.We study the almost sure(a.s.)convergence rate of the submartingale W_(n)=Z_(n)/In to its limit W,where(In)is an usually used norming sequence.We prove that under a moment condition of order p∈(1,2),W-W_(n)=o(e^(-na))a.s.for some a>0 that we find explicitly;assuming the logarithmic moment condition holds,we haveW-W_(n)=o(n^(-α))a.s..In order to obtain these results,we provide the L^(p)-convergence of(W_(n));similar conclusions hold for a bisexual branching process in a varying environment.
文摘在随机环境中两性分枝过程L^1-收敛的对数判别准则的基础上,以条件均值增长率的上确界作为规范化因子,令{ε_k (ξ_n)}和{σ_k (ξ_n)}为非增长序列,当k≥k_0时,给出了W_n→WL^2的必要条件sum from k=0 to ∞ k^(-1)σ_k (ξ_n)<∞,同时求出了在一定条件下,当k≥1时,{W_n;n∈N}依L^2-收敛到非退化到的随机变量W的充分条件是sum from k=0 to ∞ k^(-1)σ_k (ξ_n)<∞和sum from k=0 to ∞ k^(-1)ε_k (ξ_n)<∞。
