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Perturbed Markov Chains

Author

Listed:
  • Eilon Solan

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • 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)

Abstract

We obtain results on the sensitivity of the invariant measure and other statistical quantities of a Markov chain with respect to perturbations of the transition matrix. We use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.

Suggested Citation

  • Eilon Solan & Nicolas Vieille, 2002. "Perturbed Markov Chains," Working Papers hal-00593647, HAL.
    • Handle: RePEc:hal:wpaper:hal-00593647
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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.
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    Citations

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    Cited by:

    1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Approximating a Sequence of Observations by a Simple Process," Working Papers hal-00593643, HAL.
    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. , Aisdl, 2007. "Weak convergence of first-rare-event times for semi-Markov processes," OSF Preprints q95cv, Center for Open Science.
    4. 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.

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    More about this item

    Keywords

    Perturbed Markov chains; conductance;

    JEL classification:

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

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