可列非齐次循环马氏链的遍历性  

Ergodicity for countable nonhomogeneous circular Markov chains

作　　者：王蓓[1] 石志岩[1] 

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《江苏大学学报（自然科学版）》2013年第6期741-744,共4页Journal of Jiangsu University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11071104;11226210);江苏大学高级人才启动基金资助项目(11JDG116)

摘　　要：研究了一类特殊的非齐次马氏链——循环马氏链的C-遍历性.首先给出了非齐次马氏链强遍历和C-强遍历的概念,同时考虑非齐次马氏链的转移概率矩阵是循环的情形,引入可列非齐次循环马氏链的概念.若从初始时刻开始的d步转移矩阵是C-强遍历于某常数矩阵T1,则从任意时刻开始的d步转移矩阵都是C-强遍历的,且收敛到的常数矩阵均可由T1和转移矩阵给出.最后在d步转移矩阵C-强遍历的条件下,结合转移矩阵循环的性质,分段讨论后,得到可列非齐次循环马氏链的C-强遍历性质.The ergodicity for special nonhomogeneous Markov chains of circular Markov chains was studied.The definitions of strong ergodicity and C-strong ergodicity of Markov chains were introduced.The definition of countable nonhomogeneous circular Markov chain was introduced with the consideration of circular transition matrix of nonhomogeneous Markov chain.From Lemma,if the initial d-step transition matrix is C-strong ergodicity to a constant stochastic matrix T1,the d-step transition matrix at any time is C-strong ergodicity to a constant stochastic matrix which can be given by T1 and transition matrices.The C-strong ergodicity of nonhomogeneous circular Markov chain was theoretically discussed according to the C-strong ergodicity of d-step transition matrix.

关 键 词：循环马氏链 遍历性 C-强遍历 转移矩阵 收敛 常数随机矩阵 

分 类 号：O211.6[理学—概率论与数理统计]