A.S.Convergence Rate and L^(p)-Convergence of Bisexual Branching Processes in a Random Environment and Varying Environment  

作　　者：Sheng XIAO Xiang-dong LIU Ying-qiu LI 

机构地区：[1]School of economics,Jinan University,Guangzhou,510632,China [2]School of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410004,China [3]Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering,Changsha University of Science and Technology,Changsha 410004,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第2期337-353,共17页应用数学学报（英文版）

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);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)。

摘　　要：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.

关 键 词：bisexual branching process convergence rate varying environment random environment 

分 类 号：O211.65[理学—概率论与数理统计]