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Ergodic and adaptive control of hidden Markov models

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  • T. Duncan
  • B. Pasik-Duncan
  • L. Stettner

Abstract

A partially observed stochastic system is described by a discrete time pair of Markov processes. The observed state process has a transition probability that is controlled and depends on a hidden Markov process that also can be controlled. The hidden Markov process is completely observed in a closed set, which in particular can be the empty set and only observed through the other process in the complement of this closed set. An ergodic control problem is solved by a vanishing discount approach. In the case when the transition operators for the observed state process and the hidden Markov process depend on a parameter and the closed set, where the hidden Markov process is completely observed, is nonempty and recurrent an adaptive control is constructed based on this family of estimates that is almost optimal. Copyright Springer-Verlag Berlin Heidelberg 2005

Suggested Citation

  • T. Duncan & B. Pasik-Duncan & L. Stettner, 2005. "Ergodic and adaptive control of hidden Markov models," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 297-318, November.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:2:p:297-318
    DOI: 10.1007/s00186-005-0010-z
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    References listed on IDEAS

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    1. Borkar, V.S.Vivek S. & Budhiraja, Amarjit, 2004. "A further remark on dynamic programming for partially observed Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 112(1), pages 79-93, July.
    2. Ralf Korn, 1997. "Optimal Portfolios:Stochastic Models for Optimal Investment and Risk Management in Continuous Time," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 3548, August.
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    Cited by:

    1. Zhiqiang Li & Jie Xiong, 2015. "Stability of the filter with Poisson observations," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 293-313, October.
    2. Stéphane Chrétien & Juan-Pablo Ortega, 2018. "A Simple Formula for the Hilbert Metric with Respect to a Sub-Gaussian Cone," Mathematics, MDPI, vol. 6(3), pages 1-5, March.

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