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Translated Poisson Approximation for Markov Chains

Barbour, A. ; Lindvall, Torgny

In: Journal of Theoretical Probability, 2006, vol. 19, no. 3, p. 609-630

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    Titre
    • Translated Poisson Approximation for Markov Chains
    Auteur
    • Barbour, A.. Angewandte Mathematik, Winterthurerstrasse 190, 8057, Zürich, Switzerland
    • Lindvall, Torgny. School of Mathematical Sciences, Chalmers and GU, 41296, Göteborg, Sweden
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Theoretical Probability, 2006, vol. 19, no. 3, p. 609-630. Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com
    Autre version électronique
    Classification
    • Mathématiques
    Identifiant OAI-PMH
    • oai:doc.rero.ch:318945
    Summary
    The paper is concerned with approximating the distribution of a sum W of integer valued random variables Y i , 1≤ i≤ n, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson distribution, with mean and variance chosen to be close to those of W, and the error is measured with respect to the total variation norm. Error bounds comparable to those found for normal approximation with respect to the weaker Kolmogorov distance are established, provided that the distribution of the sum of the Y i 's between the successive visits of X to a reference state is aperiodic. Without this assumption, approximation in total variation cannot be expected to be good