Let a finite alphabet $\Omega $. We consider a sequence of letters from $\Omega $ generated by a discrete time semi-Markov process $\{{Z}_{\gamma};\phantom{\rule{4pt}{0ex}}\gamma \in \mathbb{N}\}.$ 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.

Keywords: discrete time semi-Markov, number of word occurrences

@article{PS_2009__13__328_0, 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://www.numdam.org/articles/10.1051/ps:2008009/} }

TY - JOUR AU - Karaliopoulou, Margarita TI - On the number of word occurrences in a semi-Markov sequence of letters JO - ESAIM: Probability and Statistics PY - 2009 SP - 328 EP - 342 VL - 13 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2008009/ DO - 10.1051/ps:2008009 LA - en ID - PS_2009__13__328_0 ER -

%0 Journal Article %A Karaliopoulou, Margarita %T On the number of word occurrences in a semi-Markov sequence of letters %J ESAIM: Probability and Statistics %D 2009 %P 328-342 %V 13 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2008009/ %R 10.1051/ps:2008009 %G en %F PS_2009__13__328_0

Karaliopoulou, Margarita. On the number of word occurrences in a semi-Markov sequence of letters. ESAIM: Probability and Statistics, Volume 13 (2009), pp. 328-342. doi : 10.1051/ps:2008009. http://www.numdam.org/articles/10.1051/ps:2008009/

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