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On a decomposition for infinite transition matrices

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Abstract

Heyman gives an interesting factorization of I-P, where P is the transition probability matrix for an ergodic Markov chain. We show that this factorization is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to be useful in the analysis of queues.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Winnipeg, Winnipeg, MB, Canada, R3B 2E9

    Yiqiang Q. Zhao, Wei Li & W. John Braun

  2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, P.R. China

    Wei Li

Authors
  1. Yiqiang Q. Zhao
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  2. Wei Li
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  3. W. John Braun
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Zhao, Y.Q., Li, W. & Braun, W.J. On a decomposition for infinite transition matrices. Queueing Systems 27, 127–130 (1997). https://doi.org/10.1023/A:1019157913836

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  • DOI: https://doi.org/10.1023/A:1019157913836

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