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Patterns generated by -order Markov chains

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  • Fisher, Evan
  • Cui, Shiliang

Abstract

We derive an expression for the expected time for a pattern to appear in higher-order Markov chains with and without a starting sequence. This yields a result for directly calculating, the first time one of a collection of patterns appears, in addition to the probability, for each pattern, that it is the first to appear.

Suggested Citation

  • Fisher, Evan & Cui, Shiliang, 2010. "Patterns generated by -order Markov chains," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1157-1166, August.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:15-16:p:1157-1166
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    References listed on IDEAS

    as
    1. Vladimir Pozdnyakov, 2008. "On occurrence of subpattern and method of gambling teams," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(1), pages 193-203, March.
    2. Benevento, Rodolfo V., 1984. "The occurrence of sequence patterns in ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 17(2), pages 369-373, July.
    3. Gerber, Hans U. & Li, Shuo-Yen Robert, 1981. "The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 11(1), pages 101-108, March.
    4. Pozdnyakov, Vladimir, 2008. "On occurrence of patterns in Markov chains: Method of gambling teams," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2762-2767, November.
    5. James Fu & W. Lou, 2006. "Waiting Time Distributions of Simple and Compound Patterns in a Sequence of r-th Order Markov Dependent Multi-state Trials," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 291-310, June.
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    Keywords

    Patterns Markov chains Waiting time;

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