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

Margarita Karaliopoulou

ESAIM: Probability and Statistics (2009)

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

Abstract

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Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process { Z γ ; γ ∈ } . 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.

How to cite

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Karaliopoulou, 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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  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.  
  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.  
  3. L.J. Guibas and A.M. Odlyzko, String Overlaps, pattern matching and nontransitive games. J. Combin. Theory Ser. A30 (1981) 183–208.  
  4. M. Lothaire, Combinatorics on Words. Addison-Wesley (1983).  
  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).  
  6. V.T. Stefanov, On Some Waiting Time Problems. J. Appl. Prob.37 (2000) 756–764.  
  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.  

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