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The intersite distances between pattern occurrences in strings generated by general discrete- and continuous-time models: an algorithmic approach

Part of:Special processesDistribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Valeri T. Stefanov
Valeri T. Stefanov*
Affiliation:
University of Western Australia
*
∗ Postal address: School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia. Email address: stefanov@maths.uwa.edu.au
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Abstract

The formation of patterns from letters of a finite alphabet is considered. The strings of letters are generated by general discrete- and continuous-time models which embrace as particular cases all models considered in the literature. The letters of the alphabet are identified by the states of either discrete- or continuous-time semi-Markov processes. A new and unifying method is introduced for evaluation of the generating functions of both the intersite distance between occurrences of an arbitrary, but fixed, pattern and the waiting time until the first occurrence of that pattern. Our method also covers in a unified way relevant and important joint generating functions. Furthermore, our results lead to an easy and efficient implementation of the relevant evaluations.

Keywords

Patternprobability generating functionsemi-Markov processrandom sum

MSC classification

Primary:60E10: Characteristic functions; other transforms
Secondary:60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 4 , September 2003, pp. 881 - 892
Copyright
Copyright © Applied Probability Trust 2003 

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