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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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