连续时间马氏链的代数及指数非常返性  

On Algebraic and Exponential Transience for Continuous-Time Markov Chains

作　　者：林娜 刘源远[1] LIN Na;LIU Yuanyuan(School of Mathematics and Statistics,Central South University,Changsha,410083,China)

机构地区：[1]中南大学数学与统计学院,长沙410083

出　　处：《应用概率统计》2022年第4期546-562,共17页Chinese Journal of Applied Probability and Statistics

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11971486,11771452);the Natural Science Foundation of Hunan(Grant Nos.2019JJ40357,2020JJ4674).

摘　　要：本文研究了连续时间马氏链的代数非常返性和指数非常返性,揭示了连续时间马氏链与其跳跃链和对偶过程之间的等价关系.运用所得结果,我们进一步得到了广义分支过程和生灭过程等连续时间马氏链的非常返性判别准则.In this paper,we investigate algebraic and exponential transience for continuous-time Markov chains(CTMCs).Equivalent relations of these transience are revealed between CTMCs and their jump chains and dual processes.The results are further applied to derive the criteria of these transience for general CTMCs,generalized Markov branching processes and birth-death processes.

关 键 词：马氏链 代数非常返 指数非常返 跳跃链 对偶过程 

分 类 号：O211.62[理学—概率论与数理统计]