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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
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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. 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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    JEL classification:

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

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