Joint distribution of pattern frequencies and multivariate Polya–Aeppli law
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 2, pp. 226-242 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. L. Rukhin. Joint distribution of pattern frequencies and multivariate Polya–Aeppli law. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 2, pp. 226-242. http://geodesic.mathdoc.fr/item/TVP_2009_54_2_a1/

[1] Barbour A. D., Chen L. H. Y., Loh W.-L., “Compound Poisson approximation for nonnegative random variables via Stein's method”, Ann. Probab., 20:4 (1992), 1843–1866 | DOI | MR | Zbl

[2] Barbour A. D., Chryssaphinou O., “Compound Poisson approximation: a user's guide”, Ann. Appl. Probab., 11:3 (2001), 964–1002 | DOI | MR | Zbl

[3] Chryssaphinou O., Papastavridis S., “A limit theorem on the number of overlapping appearances of a pattern in a sequence of independent trials”, Probab. Theory Related Fields, 79:1 (1988), 129–143 | DOI | MR

[4] Erhardsson T., “Compound Poisson approximation for counts of rare patterns in Markov chains and extreme sojourns in birth-death chains”, Ann. Appl. Probab., 10:2 (2000), 573–591 | DOI | MR | Zbl

[5] Erhardsson T., “Stein's method for Poisson and compound Poisson approximation”, An Introduction to Stein's method, eds. A. Barbour and L. H. Y. Chen, Singapore Univ. Press, Singapore, 2005, 61–113 | MR

[6] Good I. J., “The frequency count of a Markov chain and the transition to continuous time”, Ann. Math. Statist., 32 (1961), 41–48 | DOI | MR | Zbl

[7] Gulden Ya., Dzhekson D., Perechislitelnaya kombinatorika, Nauka, M., 1990, 503 pp. | MR

[8] Guibas L. J., Odlyzko A. M., “Long repetitive patterns in random sequences”, Z. Wahrscheinlichkeitstheor. verw. Geb., 53:3 (1980), 241–262 | DOI | MR | Zbl

[9] Guibas L. J., Odlyzko A. M., “Strings overlaps, pattern matching and nontransitive games”, J. Combin. Theory Ser. A, 30:2 (1970), 183–208 | DOI | MR

[10] Kemeni Dzh. Dzh., Snell Dzh. L., Konechnye tsepi Markova, Nauka, M., 1970, 271 pp.

[11] Reinert G., Schbath S., “Large compound Poisson approximations for occurrences of multiple words”, Statistics in Molecular Biology and Genetics (Seattle, 1997), IMS Lecture Notes Monogr. Ser., 33, Inst. Math. Statist., Hayward, 1999, 257–275 | MR

[12] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, M., 1963, 287 pp.

[13] Robin S., Rodolphe F., Schbath S., DNA, Words and Models: Statistics of Exceptional Words, Cambridge Univ. Press, Cambridge, 2006 | MR

[14] Roquain E., Schbath S., “Improved compound Poisson approximation for the number of occurrences of any rare word family in a stationary Markov chain”, Adv. Appl. Probab., 39:1 (2007), 128–140 | DOI | MR | Zbl

[15] Rukhin A. L., “Testing randomness: a suite of statistical procedures”, Teoriya veroyatn. i ee primen., 45:1 (2000), 137–162 | MR | Zbl

[16] “Distribution of the number of words with a prescribed frequency and tests of randomness”, Adv. Appl. Probab., 34:4 (2002), 775–797 | DOI | MR | Zbl

[17] Rukhin A. L., “Korrelyatsionnye matritsy tsepochek dlya markovskikh posledovatelnostei i testirovanie sluchainosti”, Teoriya veroyatn. i ee primen., 51:4 (2006), 712–731 | MR

[18] Szpankowski W., Average Case Analysis of Algorithms on Sequences, Wiley-Interscience, New York, 2001, 551 pp. | MR

[19] Zubkov A. M., Mikhailov V. G., “Predelnye raspredeleniya sluchainykh velichin, svyazannykh s dlinnymi povtoreniyami v posledovatelnosti nezavisimykh ispytanii”, Teoriya veroyatn. i ee primen., 19:1 (1974), 173–181 | MR | Zbl

[20] Zubkov A. M., Mikhailov V. G., “O povtoreniyakh $s$-tsepochek v posledovatelnosti zavisimykh velichin”, Teoriya veroyatn. i ee primen., 24:2 (1979), 267–279 | MR | Zbl