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Translated Poisson Approximation for Markov Chains

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An Erratum to this article was published on 15 October 2008

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.

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Authors and Affiliations

  1. Angewandte Mathematik, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    A. D. Barbour

  2. School of Mathematical Sciences, Chalmers and GU, 41296, Göteborg, Sweden

    Torgny Lindvall

Authors
  1. A. D. Barbour
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  2. Torgny Lindvall
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Correspondence to A. D. Barbour.

Additional information

An erratum to this article is available at http://dx.doi.org/10.1007/s10959-008-0190-6.

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Barbour, A.D., Lindvall, T. Translated Poisson Approximation for Markov Chains. J Theor Probab 19, 609–630 (2006). https://doi.org/10.1007/s10959-006-0047-9

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  • DOI: https://doi.org/10.1007/s10959-006-0047-9

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