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
Keywords: 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},
     year = {2009},
     publisher = {EDP Sciences},
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     doi = {10.1051/ps:2008009},
     mrnumber = {2528087},
     language = {en},
     url = {https://www.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

[1] V. Barbu, M. Boussemart and N. Limnios, Discrete time semi-Markov processes for reliability and survival analysis. Commun. Statist.-Theory and Meth. 33 (2004) 2833-2868. | Zbl | MR

[2] O. Chryssaphinou, M. Karaliopoulou and N. Limnios, On Discrete Time semi-Markov chains and applications in words occurrences. Commun. Statist.-Theory and Meth. 37 (2008) 1306-1322. | Zbl | MR

[3] L.J. Guibas and A.M. Odlyzko, String Overlaps, pattern matching and nontransitive games. J. Combin. Theory Ser. A 30 (1981) 183-208. | Zbl | MR

[4] M. Lothaire, Combinatorics on Words. Addison-Wesley (1983). | Zbl | MR

[5] G. Reinert, S. Schbath and M.S. Waterman, Probabilistic and Statistical Properties of Finite Words in Finite Sequences. In: Lothaire: Applied Combinatorics on Words. J. Berstel and D. Perrin (Eds.), Cambridge University Press (2005). | MR

[6] V.T. Stefanov, On Some Waiting Time Problems. J. Appl. Prob. 37 (2000) 756-764. | Zbl | MR

[7] V.T. Stefanov, The intersite distances between pattern occurrences in strings generated by general discrete-and continuous-time models: an algorithmic approach. J. Appl. Prob. 40 (2003) 881-892. | Zbl | MR

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