On the number of word occurrences in a semi-Markov sequence of letters
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 328-342.

Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process {Z γ ;γ∈ℕ}. 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.

DOI : 10.1051/ps:2008009
Classification : 60K10, 60K20, 60C05, 60E05
Mots-clés : discrete time semi-Markov, number of word occurrences 
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     author = {Karaliopoulou, Margarita},
     title = {On the number of word occurrences in a {semi-Markov} sequence of letters},
     journal = {ESAIM: Probability and Statistics},
     pages = {328--342},
     publisher = {EDP-Sciences},
     volume = {13},
     year = {2009},
     doi = {10.1051/ps:2008009},
     mrnumber = {2528087},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps:2008009/}
}
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Karaliopoulou, Margarita. On the number of word occurrences in a semi-Markov sequence of letters. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 328-342. doi : 10.1051/ps:2008009. http://archive.numdam.org/articles/10.1051/ps:2008009/

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