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Discounted cost optimality problem: stability with respect to weak metrics

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  • Evgueni Gordienko
  • Enrique Lemus-Rodríguez
  • Raúl Montes-de-Oca

Abstract

We find inequalities to estimate the stability (robustness) of a discounted cost optimization problem for discrete-time Markov control processes on a Borel state space. The one stage cost is allowed to be unbounded. Unlike the known results in this area we consider a perturbation of transition probabilities measured by the Kantorovich metric, closely related to the weak convergence. The results obtained make possible to estimate the vanishing rate of the stability index when approximation is made through empirical measures. Copyright Springer-Verlag 2008

Suggested Citation

  • Evgueni Gordienko & Enrique Lemus-Rodríguez & Raúl Montes-de-Oca, 2008. "Discounted cost optimality problem: stability with respect to weak metrics," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(1), pages 77-96, August.
    • Handle: RePEc:spr:mathme:v:68:y:2008:i:1:p:77-96
    DOI: 10.1007/s00186-007-0171-z
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    References listed on IDEAS

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    1. J. A. E. E. van Nunen & J. Wessels, 1978. "Note--A Note on Dynamic Programming with Unbounded Rewards," Management Science, INFORMS, vol. 24(5), pages 576-580, January.
    2. Evgueni Gordienko & Alexander Yushkevich, 2003. "Stability estimates in the problem of average optimal switching of a Markov chain," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 345-365, August.
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    Cited by:

    1. Evgueni Gordienko & Enrique Lemus-Rodríguez & Raúl Montes-de-Oca, 2009. "Average cost Markov control processes: stability with respect to the Kantorovich metric," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 13-33, August.

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