The Annals of Probability
- Ann. Probab.
- Volume 8, Number 6 (1980), 1171-1176.
A Martingale Approach to the Study of Occurrence of Sequence Patterns in Repeated Experiments
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 in Project Euclid: 19 April 2007
Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994578
Digital Object Identifier
doi:10.1214/aop/1176994578
Mathematical Reviews number (MathSciNet)
MR602390
Zentralblatt MATH identifier
0447.60006
JSTOR
links.jstor.org
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. Ann. Probab. 8 (1980), no. 6, 1171--1176. doi:10.1214/aop/1176994578. https://projecteuclid.org/euclid.aop/1176994578
