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On occurrence of patterns in Markov chains: Method of gambling teams

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  • Pozdnyakov, Vladimir

Abstract

A new martingale technique is developed to find formulas for the first two moments and generating function of the waiting time until one observes an element of a finite collection of patterns in a finite multi-state Markov chain.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2762-2767
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    References listed on IDEAS

    as
    1. Chang, Yung-Ming, 2005. "Distribution of waiting time until the rth occurrence of a compound pattern," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 29-38, November.
    2. 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.
    3. Hirano, Katuomi & Aki, Sigeo, 2003. "Number of occurrences of subpattern until the first appearance of a pattern and geometric distribution," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 259-262, November.
    4. 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.
    5. Vladimir Pozdnyakov & Joseph Glaz & Martin Kulldorff & J. Steele, 2005. "A martingale approach to scan statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(1), pages 21-37, March.
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    Cited by:

    1. Bara Kim & Jeongsim Kim & Jerim Kim, 2020. "Waiting Time Problems for Patterns in a Sequence of Multi-State Trials," Mathematics, MDPI, vol. 8(11), pages 1-16, October.
    2. Fisher, Evan & Cui, Shiliang, 2010. "Patterns generated by -order Markov chains," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1157-1166, August.
    3. Zajkowski, Krzysztof, 2014. "A note on the gambling team method," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 45-50.

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