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On the number of word occurrences in a semi-Markov sequence of letters

Published online by Cambridge University Press:  21 July 2009

Margarita Karaliopoulou
Margarita Karaliopoulou*
Affiliation:
University of Athens, Department of Mathematics, 157 84 Athens, Greece; mkaraliop@math.uoa.gr; chronis@ath.forthnet.gr
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Abstract

Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process $\{Z_{\gamma};\ \gamma\in \xN \}.$ We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.

Keywords

Discrete time semi-Markovnumber of word occurrences
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 328 - 342
Copyright
© EDP Sciences, SMAI, 2009

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References

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