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Dynamic programming for ergodic control with partial observations

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  • Borkar, V. S.

Abstract

A dynamic programming principle is derived for a discrete time Markov control process taking values in a finite dimensional space, with ergodic cost and partial observations. This uses the embedding of the process into another for which an accessible atom exists and hence a coupling argument can be used. In turn, this is used for deriving a martingale dynamic programming principle for ergodic control of partially observed diffusion processes, by 'lifting' appropriate estimates from a discrete time problem associated with it to the continuous time problem.

Suggested Citation

  • Borkar, V. S., 2003. "Dynamic programming for ergodic control with partial observations," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 293-310, February.
    • Handle: RePEc:eee:spapps:v:103:y:2003:i:2:p:293-310
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    References listed on IDEAS

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    1. Striebel, Charlotte, 1984. "Martingale conditions for the optimal control of continuous time stochastic systems," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 329-347, November.
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    Cited by:

    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. Biswas, Anup & Budhiraja, Amarjit, 2011. "Exit time and invariant measure asymptotics for small noise constrained diffusions," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 899-924.
    3. Anatoliy Swishchuk & Nikolaos Limnios, 2021. "Controlled Discrete-Time Semi-Markov Random Evolutions and Their Applications," Mathematics, MDPI, vol. 9(2), pages 1-26, January.
    4. Subhamay Saha, 2014. "Zero-Sum Stochastic Games with Partial Information and Average Payoff," Journal of Optimization Theory and Applications, Springer, vol. 160(1), pages 344-354, January.
    5. Beatris Adriana Escobedo-Trujillo & Javier Garrido-Meléndez & Gerardo Alcalá & J. D. Revuelta-Acosta, 2022. "Optimal Control with Partially Observed Regime Switching: Discounted and Average Payoffs," Mathematics, MDPI, vol. 10(12), pages 1-28, June.

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