The Annals of Probability

A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments

Shuo-Yen Robert Li

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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.

Article information

Source
Ann. Probab. Volume 8, Number 6 (1980), 1171-1176.

Dates
First available: 19 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aop/1176994578

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aop/1176994578

Mathematical Reviews number (MathSciNet)
MR602390

Zentralblatt MATH identifier
0447.60006

Subjects
Primary: 60C05: Combinatorial probability

Keywords
Leading number martingale stopping time waiting time

Citation

Li, Shuo-Yen Robert. A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments. The Annals of Probability 8 (1980), no. 6, 1171--1176. doi:10.1214/aop/1176994578. http://projecteuclid.org/euclid.aop/1176994578.


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