A note on the method of gambling team
Krzysztof Zajkowski · arXiv (Cornell University) · 2013
Gerber and Li in \cite{GeLi} formulated, using a Markov chain embedding, the system of equations which 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 by using the classical gambling team technique this system of equations could be obtained. We also present a form of solution of the system and give an example showing how first results of trials influence on probabilities that a chosen pattern precedes remaining ones in a realization of the process.