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On weak lumpability of a finite Markov chain

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  • Peng, Nan-Fu

Abstract

An irreducible and homogeneous Markov chain with finite state space is considered. Under a mild condition [Gamma] on the transition probability matrix, a necessary and sufficient condition for weak lumpability, and the characterization of the set of initial starting vectors which make it lumpable are obtained. A similar result is obtained for those transition probability matrices without the restriction of condition [Gamma].

Suggested Citation

  • Peng, Nan-Fu, 1996. "On weak lumpability of a finite Markov chain," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 313-318, May.
    • Handle: RePEc:eee:stapro:v:27:y:1996:i:4:p:313-318
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    Cited by:

    1. Stadje, Wolfgang, 2005. "The evolution of aggregated Markov chains," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 303-311, October.
    2. Jernigan, Robert W. & Baran, Robert H., 2003. "Testing lumpability in Markov chains," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 17-23, August.

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    Keywords

    Markov chain Weak lumpability;

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