确定环形Markov链的Q-矩阵

向绪言, 杨向群, 邓迎春

数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 735-750.

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数学学报 ›› 2013, Vol. 56 ›› Issue (5) : 735-750. DOI: 10.12386/A2013sxxb0073
论文

确定环形Markov链的Q-矩阵

    向绪言1, 杨向群2, 邓迎春2
作者信息 +

Identifying Q-Matrix of Cyclic Markov Chain

    Xu Yan XIANG1, Xiang Qun YANG2, Ying Chun DENG2
Author information +
文章历史 +

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.

Abstract

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

Key words

Markov chain / cyclic scheme / reversibility / transition rate / sojourn time / hitting time

引用本文

导出引用
向绪言, 杨向群, 邓迎春. 确定环形Markov链的Q-矩阵. 数学学报, 2013, 56(5): 735-750 https://doi.org/10.12386/A2013sxxb0073
Xu Yan XIANG, Xiang Qun YANG, Ying Chun DENG. Identifying Q-Matrix of Cyclic Markov Chain. Acta Mathematica Sinica, Chinese Series, 2013, 56(5): 735-750 https://doi.org/10.12386/A2013sxxb0073

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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)及教育厅优秀青年科研基金(10B073)资助项目

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