随机环境中带迁入加权分枝过程的收敛性  

Convergence of weighted branching processes with immigration in a random environment

作　　者：徐乐群 彭点江 吴金华 Xu Lequn;Peng Dianjiang;Wu Jinhua(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）》2022年第1期11-13,21,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);湖南省工程数学建模与分析重点实验室开放基金(2018MMAEZD02);湖南省水利科技项目(XSKJ2019081-13)。

摘　　要：在随机环境中加权分枝过程的研究基础上,对其进行推广,形成了随机环境中带迁入的加权分枝过程(Z_(n))。同时,研究了其规范化过程(W_(n))的a.s.收敛性,并给出了相关证明,其中W_(n)=Z_(n)/П_(n),Пn为规范化序列。On the weighted branching process in a random environment basis,the model is extended by introducing the branching process with immigration,and forms the weighted branching processes with immigration in random a environment.Meanwhile,the convergence of the normalization process(Wn)is studied,and the relevant proof is put forward,where W_(n)=Z_(n)/П_(n),Пn is the normalized sequence.

关 键 词：随机环境 带迁入加权分枝过程 A.S.收敛 

分 类 号：O211.6[理学—概率论与数理统计]