Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries
Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries
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DOI：
10.1023/a:1024125320911
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发表时间：
2001-06
影响因子：
0.9
通讯作者：
Yiqiang Q. Zhao;W. Li;W. J. Braun
中科院分区：
文献类型：
--
作者：
Yiqiang Q. Zhao;W. Li;W. J. Braun
本文利用马尔可夫链截尾技术研究了转移矩阵具有块重复项的无限状态马氏链。我们证明了一些重要的概率度量在截尾情况下是不变的。非正式地说，这些措施涉及第一次通过时间或预期访问某些级别的次数，而其他级别是禁忌的；它们与所谓的马尔可夫链基本矩阵密切相关，这里也研究了该矩阵。得到了转移矩阵块的特征方程的因式分解定理。基于谱分析，或基于基本矩阵的一个性质，给出了这种马尔可夫链是正递归、零递归或瞬变的充要条件。得到了包括平稳概率向量和基本矩阵在内的关键概率度量的显式表达式，这些表达式可用于开发计算这些度量的各种递归算法。
In this paper, we use the Markov chain censoring technique to study infinite state Markov chains whose transition matrices possess block-repeating entries. We demonstrate that a number of important probabilistic measures are invariant under censoring. Informally speaking, these measures involve first passage times or expected numbers of visits to certain levels where other levels are taboo; they are closely related to the so-called fundamental matrix of the Markov chain which is also studied here. Factorization theorems for the characteristic equation of the blocks of the transition matrix are obtained. Necessary and sufficient conditions are derived for such a Markov chain to be positive recurrent, null recurrent, or transient based either on spectral analysis, or on a property of the fundamental matrix. Explicit expressions are obtained for key probabilistic measures, including the stationary probability vector and the fundamental matrix, which could be potentially used to develop various recursive algorithms for computing these measures.