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number of word occurrences

ESAIM: Probability and Statistics (1)

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On the number of word occurrencesin a semi-Markov sequence of letters
Margarita Karaliopoulou
Journal:

ESAIM: Probability and Statistics / Volume 13 / July 2009

Published online by Cambridge University Press:

21 July 2009, pp. 328-342

Print publication:

July 2009
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Let a finite alphabet Ω. We consider a sequence of letters from Ωgenerated by a discrete time semi-Markov process $\{Z_{\gamma};\ \gamma\in \xN \}.$ Wederive the probability of a word occurrence in the sequence. We also obtain resultsfor the mean and variance of the number of overlapping occurrences of a word in afinite discrete time semi-Markov sequence of letters under certain conditions.