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

Part of:Distribution theory - ProbabilityCombinatorial probabilityMarkov processesDistribution theory

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 S 0 and S 1 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 S 0 and between successive occurrences of S 0 and S 1 and of the waiting time until the rth occurrence of S 0 are also given.

Keywords

Patternsooner and later waiting timeMarkov chainoverlapping structureDNA sequence analysis

MSC classification

Primary:60E05: Distributions60C05: Combinatorial probability
Secondary:62E15: Exact distribution theory60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Information

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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