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
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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
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- 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.
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- M. Lothaire, Combinatorics on Words. Addison-Wesley (1983).
- 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.
- 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.
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