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On weak lumpability of denumerable Markov chains

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  • Ledoux, James

Abstract

We consider weak lumpability of denumerable Markov chains evolving in discrete or continuous time. Specifically, we study the properties of the set of all initial distributions of the starting chain leading to an aggregated homogeneous Markov chain with respect to a partition of the state space.

Suggested Citation

  • Ledoux, James, 1995. "On weak lumpability of denumerable Markov chains," Statistics & Probability Letters, Elsevier, vol. 25(4), pages 329-339, December.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:4:p:329-339
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    References listed on IDEAS

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    1. Rubino, Gerardo & Sericola, Bruno, 1993. "A finite characterization of weak lumpable Markov processes. Part II: The continuous time case," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 115-125, March.
    2. Rubino, Gerardo & Sericola, Bruno, 1991. "A finite characterization of weak lumpable Markov processes. Part I: The discrete time case," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 195-204, August.
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    Cited by:

    1. Spreij, Peter, 2001. "On the Markov property of a finite hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 279-288, April.
    2. Levi John Wolf & Sergio Rey, 2016. "On the lumpability of regional income convergence," Letters in Spatial and Resource Sciences, Springer, vol. 9(3), pages 265-275, October.

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    1. Spreij, Peter, 2001. "On the Markov property of a finite hidden Markov chain," Statistics & Probability Letters, Elsevier, vol. 52(3), pages 279-288, April.
    2. Stadje, Wolfgang, 2005. "The evolution of aggregated Markov chains," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 303-311, October.
    3. Levi John Wolf & Sergio Rey, 2016. "On the lumpability of regional income convergence," Letters in Spatial and Resource Sciences, Springer, vol. 9(3), pages 265-275, October.

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