A note on the gambling team method

Krzysztof Zajkowski

doi:10.1016/j.spl.2013.11.003

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arXiv · 1310.4316

A note on the gambling team method

Krzysztof Zajkowski

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Abstract

Gerber and Li in \cite{GeLi} 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 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 remaining ones in a realization of the process.

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Krzysztof Zajkowski. 2013-12-03. A note on the gambling team method. https://doi.org/10.1016/j.spl.2013.11.003

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