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A note on the gambling team method

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  • Zajkowski, Krzysztof

Abstract

Gerber and Li (1981) formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent repeated experiments when the initial outcomes of the process are known. We show how this system of equations can be obtained by using the classical gambling team technique. We also present a form of solution of the system and give an example showing how first results of trials influence the probabilities that a chosen pattern precedes the remaining ones in a realization of the process.

Suggested Citation

  • Zajkowski, Krzysztof, 2014. "A note on the gambling team method," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 45-50.
    • Handle: RePEc:eee:stapro:v:85:y:2014:i:c:p:45-50
    DOI: 10.1016/j.spl.2013.11.003
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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