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December, 1980 A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments
Shuo-Yen Robert Li
Ann. Probab. 8(6): 1171-1176 (December, 1980). DOI: 10.1214/aop/1176994578

Abstract

We apply the concept of stopping times of martingales to problems in classical probability theory regarding the occurrence of sequence patterns in repeated experiments. For every finite collection of sequences of possible outcomes, we compute the expected waiting time till one of them is observed in a run of experiments. Also we compute the probability for each sequence to be the first to appear. The main result, with a transparent proof, is a generalization of some well-known facts on Bernoulli process including formulas of Feller and the "leading number" algorithm of Conway.

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Shuo-Yen Robert Li. "A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments." Ann. Probab. 8 (6) 1171 - 1176, December, 1980. https://doi.org/10.1214/aop/1176994578

Information

Published: December, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0447.60006
MathSciNet: MR602390
Digital Object Identifier: 10.1214/aop/1176994578

Subjects:
Primary: 60C05

Rights: Copyright © 1980 Institute of Mathematical Statistics

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Vol.8 • No. 6 • December, 1980
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