The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain

Hans U. Gerber and Shuo-Yen Robert Li

Stochastic Processes and their Applications, 1981, vol. 11, issue 1, 101-108

Abstract: A martingale argument is used to derive the generating function of the number of i.i.d. experiments it takes to observe a given string of outcomes for the first time. Then, a more general problem can be studied: How many trials does it take to observe a member of a finite set of strings for the first time? It is shown how the answer can be obtained within the framework of hitting times in a Markov chain. For these, a result of independent interest is derived.

Keywords: Hitting; times; sequence; patterns; runs; martingale (search for similar items in EconPapers)
Date: 1981
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Citations: View citations in EconPapers (7)

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