Compound Poisson approximation of word counts in DNA sequences
ESAIM: Probability and Statistics, Tome 1 (1997), pp. 1-16. 
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     volume = {1},
     year = {1997},
     mrnumber = {1382515},
     zbl = {0869.60067},
     language = {en},
     url = {http://archive.numdam.org/item/PS_1997__1__1_0/}
}
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Schbath, Sophie. Compound Poisson approximation of word counts in DNA sequences. ESAIM: Probability and Statistics, Tome 1 (1997), pp. 1-16. http://archive.numdam.org/item/PS_1997__1__1_0/

Arratia, R., Goldstein, L. and Gordon, L. ( 1989). Two moments suffice for Poisson approximations : the Chen-Stein method. Ann. Prob. 17 9-25. | MR | Zbl

Arratia, R., Goldstein, L. and Gordon, L. ( 1990). Poisson approximation and the Chen-Stein method. Statistical Science. 5 403-434. | MR | Zbl

Barbour, A. D., Chen, L. H. Y. and Loh, W.-L. ( 1992a). Compound Poisson approximation for nonnegative random variables via Stein's method. Ann. Prob. 20 1843-1866. | MR | Zbl

Barbour, A. D., Holst, L. and Janson, S. ( 1992b). Poisson approximation. Oxford-University Press. | MR | Zbl

Chen, L. H. Y. ( 1975). Poisson approximation for dependent trials. Ann. Prob. 3 534-545. | MR | Zbl

Chryssaphinou, O. and Papastavridis, S. ( 1988a). A limit theorem for the number of non-overlapping occurrences of a pattern in a sequence of independent trials. J. Appl. Prob. 25 428-431. | MR | Zbl

Chryssaphinou, O. and Papastavridis, S. ( 1988b). A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials. Prob. Theory Rel. Fields. 79 129-143. | MR | Zbl

Doukhan, P. ( 1994). Mixing: Properties and Examples. L.N.S. 85, Springer-Verlag. | MR | Zbl

Fu, J. C. ( 1993). Poisson convergence in reliability of a large linearly connected system as related to coin tossing. Statistica Sinica. 3 261-275. | MR | Zbl

Geske, M. X., Godbole, A. P., Schaffner, A. A., Skolnick, A. M. and Wallstrom, G. L. ( 1995). Compound Poisson approximations for word patterns under Markovian hypotheses. J. Appl. Prob. To appear. | MR | Zbl

Godbole, A. P. ( 1991). Poisson approximations for runs and patterns of rare events. Adv. Appl. Prob. 23 851-865. | MR | Zbl

Godbole, A. P. and Schaffner, A. A. ( 1993). Improved poisson approximations for word patterns. Adv. Appl. Prob. 25 334-347. | MR | Zbl

Guibas, L. J. and Odlyzko, A. M. ( 1981). Periods in strings. J. Combinatorial Theory A. 30 19-42. | MR | Zbl

Hirano, K. and Aki, S. ( 1993). On number of occurrences of sucess runs of specified length in a two-state Markov chain. Statistica Sinica. 3 313-320. | MR | Zbl

Karlin, S. and Ost, F. ( 1987). Counts of long aligned word matches among random letter sequences. Ann. Prob. 19 293-351. | MR | Zbl

Lothaire, M. ( 1983). Combinatorics on words. Addison-Wesley. | MR | Zbl

Prum, B., Rodolphe, F. and Turckheim, É.DE ( 1995). Finding words with unexpected frequencies in DNA sequences. J. R. Statist. Soc. B. 57 205-220. | MR | Zbl

Roos, M. ( 1994). Stein's method for compound Poisson approximation : the local approach. Ann. Appl. Prob. 4 1177-1187. | MR | Zbl

Schbath, S. ( 1995). Étude asymptotique du nombre d'occurrences d'un mot dans une chaîne de Markov et application à la recherche de mots de fréquence exceptionnelle dans les séquences d'ADN. PhD thesis, Université René Descartes, Paris V.

Schbath, S., Prum, B. and Turckheim, É. DE ( 1995). Exceptional motifs in different Markov chain models for a statistical analysis of DNA sequences. J. Comp. Biol. 2 417-437.

Trifonov, E. N. ( 1989). The multiple codes of nucleotide sequences. Bull. Math. Biol. 51 417-432. | MR | Zbl