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 $\Omega$. We consider a sequence of letters from $\Omega$ generated by a discrete time semi-Markov process $\left\{{Z}_{\gamma };\phantom{\rule{4pt}{0ex}}\gamma \in ℕ\right\}.$ 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 : https://doi.org/10.1051/ps:2008009
Classification : 60K10,  60K20,  60C05,  60E05
Mots clés : 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
DA  - 2009///
SP  - 328
EP  - 342
VL  - 13
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ps:2008009/
UR  - https://www.ams.org/mathscinet-getitem?mr=2528087
UR  - https://doi.org/10.1051/ps:2008009
DO  - 10.1051/ps:2008009
LA  - en
ID  - PS_2009__13__328_0
ER  - 
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://www.numdam.org/articles/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. | MR 2138658 | Zbl 1089.60525

[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. | MR 2440442 | Zbl 1167.60357

[3] L.J. Guibas and A.M. Odlyzko, String Overlaps, pattern matching and nontransitive games. J. Combin. Theory Ser. A 30 (1981) 183-208. | MR 611250 | Zbl 0454.68109

[4] M. Lothaire, Combinatorics on Words. Addison-Wesley (1983). | MR 675953 | Zbl 0514.20045

[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 2165687

[6] V.T. Stefanov, On Some Waiting Time Problems. J. Appl. Prob. 37 (2000) 756-764. | MR 1782451 | Zbl 0969.60021

[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. | MR 2012674 | Zbl 1054.60022

Cité par Sources :