确定环形Markov链的Q-矩阵  

Identifying Q-Matrix of Cyclic Markov Chain

作　　者：向绪言[1] 杨向群[2] 邓迎春[2] 

机构地区：[1]湖南文理学院数学与计算科学学院,常德415000 [2]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《数学学报（中文版）》2013年第5期735-750,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11171101);湖南省自然科学基金(09JJ6016;13JJ3114);教育厅优秀青年科研基金(10B073)资助项目

摘　　要：给出了Markov链中任一状态集的逗留时间或击中时间的分布(混合指数分布),以及其分布的各阶微分与Q-矩阵之间的约束方程组.利用该约束关系及环形链结构的先验信息,采用Markov链反演方法证明了:对于有限状态环形Markov链,其Q-矩阵能由其中任意两个相邻状态的逗留时间和击中时间分布唯一决定,并给出了相应的算法.The sojourn time and hitting time distributions（the mixtures of exponential distributions） are provided for a given subset of state space of Markov chain.Then the derivatives of these distributions at t = 0 are related to the Q-matrix.Based on the constraint relationships and the priori information from the structure of Markov chain, an inversion approach is developed to identify the transition rates from the parameters characterizing these distributions.For cyclic Markov chain with finite states,as a result, it is derived that its Q-matrix can be uniquely determined by the distributions of their sojourn time and hitting time at arbitrary two adjacent states.The corresponding algorithm is included to show the validity of such approach.

关 键 词：MARKOV链 环状模型 可逆性 Q-矩阵 逗留时间 击中时间 

分 类 号：O211.62[理学—概率论与数理统计]