随机环境中乘积受控分枝过程的方差  

The variance of multiplicative controlled branching process in a random environment

作　　者：何永超 李培汉 邓琳 He Yongchao;Li Peihan;Deng Lin(College of Mathematics and Statistics,Changsha University of Science and Technology,Changsha 410114,China)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《湖南文理学院学报（自然科学版）》2023年第1期1-3,12,共4页Journal of Hunan University of Arts and Science(Science and Technology)

基　　金：国家自然科学基金重点项目(11731012)。

摘　　要：在随机环境中乘积受控分枝过程的研究基础上,考虑乘积因子取整数时其规范化过程Wn的方差Var_(ξ)(W_(k))及其收敛性,并予以了详细的证明,其中规范化过程为W_(n)=Z_(n)/P_(n),P_(n)是规范化序列,是随机环境分枝过程相关结论的拓展。On the basis of the research on the multiplicative controlled branching process in a random environment,the variance and the convergence of the normalization process W_(n) are considered when the product factor of the model is an integer,and the detailed proof is given.The normalization process is W_(n)=Z_(n)/P_(n),P_(n),and P_(n) is the normalized sequence,it is the extension of the branching process in a random environment.

关 键 词：随机环境 乘积受控分枝过程 方差 乘积因子 

分 类 号：O211.6[理学—概率论与数理统计]