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Approximating a sequence of observations by a simple process

Author

Listed:
  • Dinah Rosenberg

    (LAGA - Laboratoire Analyse, Géométrie et Applications - UP8 - Université Paris 8 Vincennes-Saint-Denis - UP13 - Université Paris 13 - Institut Galilée - CNRS - Centre National de la Recherche Scientifique)

  • 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

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step transitions along a realization from the approximating process, are close to that of the given sequence. We generalize the result to the case where the one-step transitions are required to be in given polyhedra.

Suggested Citation

  • Dinah Rosenberg & Nicolas Vieille & Eilon Solan, 2004. "Approximating a sequence of observations by a simple process," Post-Print hal-00464946, HAL.
    • Handle: RePEc:hal:journl:hal-00464946
    DOI: 10.1214/009053604000000643
    as

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    References listed on IDEAS

    as
    1. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832, Elsevier.
    2. 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.
    3. Eilon Solan & Nicolas Vieille, 2002. "Perturbed Markov Chains," Discussion Papers 1342, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Solan, Eilon, 2018. "Acceptable strategy profiles in stochastic games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 523-540.

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    More about this item

    Keywords

    Markov chains; data approximation; nonhomogenous Markov chains; hidden Markov chains;
    All these keywords.

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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