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Perturbed Markov chains

Author

Listed:
  • Nicolas Vieille

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eilon Solan

    (TAU - Tel Aviv University)

Abstract

We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

Suggested Citation

  • Nicolas Vieille & Eilon Solan, 2003. "Perturbed Markov chains," Post-Print hal-00464967, HAL.
    • Handle: RePEc:hal:journl:hal-00464967
    DOI: 10.1239/jap/1044476830
    as

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    References listed on IDEAS

    as
    1. Nicolas Vieille, 2000. "Small perturbations and stochastic games," Post-Print hal-00481409, HAL.
    2. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. repec:dau:papers:123456789/6019 is not listed on IDEAS
    5. Seneta, E., 1993. "Sensitivity of finite Markov chains under perturbation," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 163-168, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Approximating a sequence of observations by a simple process," HEC Research Papers Series 756, HEC Paris.
    2. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    3. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Approximating a Sequence of Approximations by a Simple Process," Discussion Papers 1345, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. , Aisdl, 2007. "Weak convergence of first-rare-event times for semi-Markov processes," OSF Preprints q95cv, Center for Open Science.

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    More about this item

    Keywords

    Markov chains; stationary distribution; exit distribution; conductance; sensitivity analysis; perturbation theory; stability of a Markov chain;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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