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Uniform ergodicity of continuous-time controlled Markov chains: A survey and new results

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  • Tomás Prieto-Rumeau

    (UNED)

  • Onésimo Hernández-Lerma

    (CINVESTAV-IPN)

Abstract

We make a review of several variants of ergodicity for continuous-time Markov chains on a countable state space. These include strong ergodicity, ergodicity in weighted-norm spaces, exponential and subexponential ergodicity. We also study uniform exponential ergodicity for continuous-time controlled Markov chains, as a tool to deal with average reward and related optimality criteria. A discussion on the corresponding ergodicity properties is made, and an application to a controlled population system is shown.

Suggested Citation

  • Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2016. "Uniform ergodicity of continuous-time controlled Markov chains: A survey and new results," Annals of Operations Research, Springer, vol. 241(1), pages 249-293, June.
    • Handle: RePEc:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-012-1184-4
    DOI: 10.1007/s10479-012-1184-4
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    References listed on IDEAS

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    1. Michael N. Katehakis & Cyrus Derman, 1989. "On the Maintenance of Systems Composed of Highly Reliable Components," Management Science, INFORMS, vol. 35(5), pages 551-560, May.
    2. Xianping Guo & Alexei Piunovskiy, 2011. "Discounted Continuous-Time Markov Decision Processes with Constraints: Unbounded Transition and Loss Rates," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 105-132, February.
    3. Tomás Prieto-Rumeau & Onésimo Hernández-Lerma, 2005. "The Laurent series, sensitive discount and Blackwell optimality for continuous-time controlled Markov chains," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(1), pages 123-145, March.
    4. R. Dekker & A. Hordijk & F. M. Spieksma, 1994. "On the Relation Between Recurrence and Ergodicity Properties in Denumerable Markov Decision Chains," Mathematics of Operations Research, INFORMS, vol. 19(3), pages 539-559, August.
    5. Mao, Yong-Hua, 2006. "Convergence rates in strong ergodicity for Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1964-1976, December.
    6. Coquet, François & Mackevicius, Vigirdas & Mémin, Jean, 1999. "Corrigendum to "Stability in of martingales and backward equations under discretization of filtration": [Stochastic Processes and their Applications 75 (1998) 235-248]," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 335-338, August.
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    Cited by:

    1. Xianping Guo & Yi Zhang, 2016. "Optimality of Mixed Policies for Average Continuous-Time Markov Decision Processes with Constraints," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1276-1296, November.

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