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A limit theorem for the number of non-overlapping occurrences of a pattern in a sequence of independent trials

Published online by Cambridge University Press:  14 July 2016

O. Chryssaphinou  and
S. Papastavridis
O. Chryssaphinou*
Affiliation:
University of Athens
S. Papastavridis*
Affiliation:
University of Patras
*
∗Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, 15710 Athens, Greece.
∗∗Postal address: Applied Mathematics Division, University of Patras, 26110 Patras, Greece.
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Abstract

A sequence of independent experiments is performed, each producing a letter from a given alphabet. Using a result by Barbour and Eagleson (1984) we prove that under general conditions the number of non-overlapping occurrences of long recurrent patterns has approximately a Poisson distribution.

Keywords

RECURRENT PATTERNSPOISSON DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 25 , Issue 2 , June 1988 , pp. 428 - 431
Copyright
Copyright © Applied Probability Trust 1988 

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References

Barbour, A. D. and Eagleson, G. K. (1983) Poisson approximation for some statistics based on exchangeable trials. Adv. Appl. Prob. 15, 585–600.Google Scholar
Barbour, A. D. and Eagleson, G. K. (1984) Poisson convergence for dissociated statistics. J.R. Statist. Soc. B46, 397–402.Google Scholar
Benevento, R. V. (1984) The occurrence of sequence patterns in ergodic Markov chains. Stoch. Proc. Appl. 17, 369–373.Google Scholar
Blom, G. (1982) On the mean number of random digits until a given sequence occurs. J. Appl. Prob. 19, 136–143.Google Scholar
Blom, G. and Thorburn, D. (1982) How many random digits are required until given sequences are obtained? J. Appl. Prob. 19, 518–531.Google Scholar
Breen, S., Waterman, M. S. and Zhang, N. (1985) Renewal theory for several patterns. J. Appl. Prob. 22, 228–234.CrossRefGoogle Scholar
Feller, W. (1968) An Introduction to Probability and its Applications , 3rd. edn. Wiley, New York.Google Scholar
Földes, A. (1979) The limit distribution of the length of the longest head-run. Period. Math. Hungar. 10 (4), 301–310.Google Scholar
Guibas, L. J. and Odlyzko, A. M. (1978) Maximal prefix-synchronized codes. SIAM J. Appl. Math. 35, 401–418.Google Scholar
Guibas, L. J. and Odlyzko, A. M. (1980) Long repetitive patterns in random sequences. Z. Wahrscheinlichkeitsth. 53, 241–262.Google Scholar
Guibas, L. J. and Odlyzko, A. M. (1981) Periods of strings. J. Comb. Theory A 30, 19–42.Google Scholar
Guibas, L. J. and Odlyzko, A. M. (1981) String overlaps, pattern matching, and nontransitive games. J. Comb. Theory A 30, 183–208.Google Scholar
Rajarshi, M. B. (1974) Success runs in a two-state Markov chain. J. Appl. Prob. 11, 190–192.Google Scholar
Samarova, S. S. (1981) On the length of the longest head-run for a Markov chain with two states. Theory Prob. Appl. 26, 498–509.Google Scholar
Soltani, A. R. and Khodadadi, A. (1986) Run probabilities and the motion of a particle on a given path. J. Appl. Prob. 23, 28–41.Google Scholar