生灭过程的两类拟平稳分布  

Two Types of Quasi-stationary Distributions for Birth-death Processes

作　　者：朱依霞 ZHU Yixia(School of Mathematics and Statistics,Hunan University of Finance and Economics,Changsha 410205,China)

机构地区：[1]湖南财政经济学院数学与统计学院,长沙410205

出　　处：《湖北民族大学学报（自然科学版）》2021年第4期446-450,共5页Journal of Hubei Minzu University:Natural Science Edition

基　　金：湖南省教育厅科学研究项目(18C0974);湖南省普通高等学校课程思政建设研究项目(HNKCSZ-2020-0694).

摘　　要：主要研究生灭过程的两类拟平稳分布:双重极限条件的拟平稳分布和极限条件平均比值的拟平稳分布.当拟平稳分布是从一个概率分布出发时,研究得到这两类拟平稳分布的存在性和唯一性的充分条件以及解决拟平稳分布唯一时候的吸引域问题.In this paper,we mainly study two types of quasi stationary distributions for birth and death processes:doubly limiting conditional quasi-stationary distribution and limiting conditional mean ratio quasi-stationary distribution.When the quasi stationary distribution starts from a probability distribution,we obtain the sufficient conditions for the existence and uniqueness of the two types of quasi stationary distributions and solve the problem of the domain of attraction when the quasi stationary distribution is unique.

关 键 词：马尔可夫链 生灭过程 拟平稳分布 吸引域 对偶过程 

分 类 号：O211.6[理学—概率论与数理统计]