Censoring, Factorizations, and Spectral Analysis for Transition Matrices with Block-Repeating Entries

Yiqiang Q. Zhao (), Wei Li () and W. John Braun ()
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Yiqiang Q. Zhao: School of Mathematics and Statistics, Carleton University
Wei Li: Department of Electical and Computer Engineering, University of Louisiana at Lafayette
W. John Braun: Department of Statistical and Actuarial Sciences, University of Western Ontario

No lrsp-TRS355, RePAd Working Paper Series from Département des sciences administratives, UQO

Abstract: 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 recursivealgorithms for computing these measures.

Keywords: block-Toeplitz transition matrices; factorization of characteristic functions; spectral analysis; fundamental matrix; conditions of recurrence and transience. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Date: Written 2001-06-27

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