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A Poisson Limit Theorem on the Number of Appearances of a Pattern in a Markov Chain

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Athens Conference on Applied Probability and Time Series Analysis

Part of the book series: Lecture Notes in Statistics ((LNS,volume 114))

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Abstract

A sequence of Markov dependent trials is performed, each one of them producing a letter from a given finite alphabet. Under quite general conditions we prove that the number of non—overlapping occurrences of long patterns approximates a Poisson distribution.

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Author information

Authors and Affiliations

  1. University of Athens, Greece

    Ourania Chryssaphinou & Stavros Papastavridis

Authors
  1. Ourania Chryssaphinou
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  2. Stavros Papastavridis
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Editor information

Editors and Affiliations

  1. Stochastic Analysis Program, SMS, Australian National University, Canberra, ACT, 0200, Australia

    C. C. Heyde

  2. Academy of Sciences, Mathematical Institute, Vavilov Street 42, Moscow, 333, Russia

    Yu V. Prohorov

  3. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Ronald Pyke

  4. Department of Statistics and Applied Probability, University of California, Santa Barbara, Santa Barbara, CA, 93106, USA

    S. T. Rachev

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© 1996 Springer Science+Business Media New York

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Chryssaphinou, O., Papastavridis, S. (1996). A Poisson Limit Theorem on the Number of Appearances of a Pattern in a Markov Chain. In: Heyde, C.C., Prohorov, Y.V., Pyke, R., Rachev, S.T. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0749-8_6

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  • DOI: https://doi.org/10.1007/978-1-4612-0749-8_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94788-4

  • Online ISBN: 978-1-4612-0749-8

  • eBook Packages: Springer Book Archive

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