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Sooner and later waiting time problems for patterns in Markov dependent trials

Part of: Combinatorial probability Distribution theory - Probability Distribution theory Markov processes

Published online by Cambridge University Press:  14 July 2016

Qing Han  and
Katuomi Hirano
Qing Han*
Affiliation:
Shanghai University of Finance and Economics
Katuomi Hirano*
Affiliation:
The Institute of Statistical Mathematics, Tokyo
*
∗ Postal address: School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China. Email address: qhan@mail.shufe.edu.cn
∗∗ Postal address: The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo, 106-8569, Japan.
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Abstract

In this paper, we investigate sooner and later waiting time problems for patterns S0 and S1 in multistate Markov dependent trials. The probability functions and the probability generating functions of the sooner and later waiting time random variables are studied. Further, the probability generating functions of the distributions of distances between successive occurrences of S0 and between successive occurrences of S0 and S1 and of the waiting time until the rth occurrence of S0 are also given.

Keywords

Patternsooner and later waiting timeMarkov chainoverlapping structureDNA sequence analysis

MSC classification

Primary: 60E05: Distributions 60C05: Combinatorial probability
Secondary: 62E15: Exact distribution theory 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 73 - 86
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

Supported by the Foundation for Key University Teachers by the Ministry of Education, China.

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