# On the number of word occurrences in a semi-Markov sequence of letters

ESAIM: Probability and Statistics (2009)

- Volume: 13, page 328-342
- ISSN: 1292-8100

## Access Full Article

top## Abstract

top## How to cite

topKaraliopoulou, Margarita. "On the number of word occurrences in a semi-Markov sequence of letters." ESAIM: Probability and Statistics 13 (2009): 328-342. <http://eudml.org/doc/250657>.

@article{Karaliopoulou2009,

abstract = {
Let a finite alphabet Ω. We consider a sequence of letters from Ω
generated by a discrete time semi-Markov process $\\{Z_\{\gamma\};\ \gamma\in \xN \\}.$ 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.
},

author = {Karaliopoulou, Margarita},

journal = {ESAIM: Probability and Statistics},

keywords = {Discrete time semi-Markov; number of word occurrences; discrete time semi-Markov},

language = {eng},

month = {7},

pages = {328-342},

publisher = {EDP Sciences},

title = {On the number of word occurrences in a semi-Markov sequence of letters},

url = {http://eudml.org/doc/250657},

volume = {13},

year = {2009},

}

TY - JOUR

AU - Karaliopoulou, Margarita

TI - On the number of word occurrences in a semi-Markov sequence of letters

JO - ESAIM: Probability and Statistics

DA - 2009/7//

PB - EDP Sciences

VL - 13

SP - 328

EP - 342

AB -
Let a finite alphabet Ω. We consider a sequence of letters from Ω
generated by a discrete time semi-Markov process $\{Z_{\gamma};\ \gamma\in \xN \}.$ 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.

LA - eng

KW - Discrete time semi-Markov; number of word occurrences; discrete time semi-Markov

UR - http://eudml.org/doc/250657

ER -

## References

top- 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. Zbl1089.60525
- 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. Zbl1167.60357
- L.J. Guibas and A.M. Odlyzko, String Overlaps, pattern matching and nontransitive games. J. Combin. Theory Ser. A30 (1981) 183–208. Zbl0454.68109
- M. Lothaire, Combinatorics on Words. Addison-Wesley (1983). Zbl0514.20045
- 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).
- V.T. Stefanov, On Some Waiting Time Problems. J. Appl. Prob.37 (2000) 756–764. Zbl0969.60021
- 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. Zbl1054.60022

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.