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The evolution of aggregated Markov chains

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  • Stadje, Wolfgang

Abstract

For a stationary two-sided Markov chain with finite state-space I and a partition we consider the aggregated sequence defined by Yn=[nu] if Xn[set membership, variant]I[nu], which is also stationary but in general not Markovian. We present a tractable way to determine the transition probabilities of , either given a finite part of its past or given its infinite past. These probabilities are linked to the Radon-Nikodym derivative of PUnXn=i with respect to PUn, where .

Suggested Citation

  • Stadje, Wolfgang, 2005. "The evolution of aggregated Markov chains," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 303-311, October.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:4:p:303-311
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    References listed on IDEAS

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    1. Peng, Nan-Fu, 1996. "On weak lumpability of a finite Markov chain," Statistics & Probability Letters, Elsevier, vol. 27(4), pages 313-318, May.
    2. Spreij, Peter, 2003. "On hidden Markov chains and finite stochastic systems," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 189-201, April.
    3. Jernigan, Robert W. & Baran, Robert H., 2003. "Testing lumpability in Markov chains," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 17-23, August.
    4. Yasemin Serin & Zeynep Muge Avsar, 1997. "Markov decision processes with restricted observations: Finite horizon case," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(5), pages 439-456, August.
    5. Pruscha, Helmut & Theodorescu, Radu, 1977. "Functions of event variables of a random system with complete connections," Journal of Multivariate Analysis, Elsevier, vol. 7(2), pages 336-362, June.
    6. 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. Berghout, Steven & Verbitskiy, Evgeny, 2021. "On regularity of functions of Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 134(C), pages 29-54.

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