On the asymptotic normality conditions for the number of repetitions in a stationary random sequence

References

[1] Borovkov A.A., Probability Theory, New York: Gordon & Breach, 1998, 474 pp.Suche in Google Scholar

[2] Zubkov A.M., Mikhailov V.G., “Repetitions of s-tuples in a sequence of independent trials”, Theory Probab. Appl., 24:2 (1979), 269–282.10.1137/1124034Suche in Google Scholar

[3] Zubkov A.M., Mikhailov V.G., “Limit distributions of random variables associated with long duplications in a sequence of independent trials”, Theory Probab. Appl., 19:1 (1974), 172–179.10.1137/1119017Suche in Google Scholar

[4] Ibragimov I. A., Linnik Yu. V., Independent and stationary sequences of random variables, Groningen: Wolters-Noordhof, 1971, 443 pp.Suche in Google Scholar

[5] Mikhailov V.G., “On a theorem of Janson”, Theory Probab. Appl., 36:1 (1991), 173–176.10.1137/1136018Suche in Google Scholar

[6] Mikhailov V.G., “Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain”, Discrete Math. Appl., 26:2 (2016), 105–113.10.1515/dma-2016-0008Suche in Google Scholar

[7] Mikhailov V.G., Shoytov A.M., “On repetitions of long tuples in a Markov chain”, Discrete Math. Appl., 25:5 (2015), 295–303.10.1515/dma-2015-0028Suche in Google Scholar

[8] Mikhailov V.G., Shoytov A.M., “On multiple repetitions of long tuples in a Markov chain”, 6:3 (2015), 117–134 (in Russian).10.4213/mvk163Suche in Google Scholar

[9] Tikhomirova M.I., Chistjakov V.P., “On the asymptotic normality of some sums of dependent random variables”, Discrete Math. Appl., 27:2 (2017), 123–129.10.1515/dma-2017-0015Suche in Google Scholar

[10] Shiryaev A.N., Probability-1, Springer-Verlag, New York, 2016, 486 pp.10.1007/978-0-387-72206-1Suche in Google Scholar

[11] Chen L.H.Y., Qi-Man Shao, Stein’s method for normal approximation, World Scientific, 2004.Suche in Google Scholar

[12] Dehling H., “Limit theorems for dependent U-statistics”, Lecture Notes in Statistics, 187 (2006), 65–86.10.1007/0-387-36062-X_3Suche in Google Scholar

[13] Feray V., “Weighted dependency graphs”, Electron. J. Probab., 23:93 (2018).10.1214/18-EJP222Suche in Google Scholar

[14] Feray V., “Central limit theorems for patterns in multiset permutations and set partitions”, Ann. Appl. Probab., 3:1 (2020), 287–323.10.1214/19-AAP1502Suche in Google Scholar

[15] Yoshihara K., “Limiting behavior of U-statistics for stationary absolutely regular process”, Z. Wahrsch. Verw. Gebiete, 35(1976), 235–252.10.1007/BF00532676Suche in Google Scholar

[16] Janson S., “Normal convergence by higher semiinvariants with applications to sums of dependent random variables and random graphs”, Ann. Probab., 16:1 (1988), 305–312.10.1214/aop/1176991903Suche in Google Scholar

[17] Koroljuk V.S., Borovskych Yu.V., Theory of U-statistics, Springer, Dordrecht, Netherlands, 1994.10.1007/978-94-017-3515-5Suche in Google Scholar

[18] Karlin S., Ost F., “Maximal length of common words among random letter sequences”, Ann. Probab., 16(2) (1988), 535–563.10.1214/aop/1176991772Suche in Google Scholar

[19] Mikhailov V. G., Mezhennaya N. M., “Normal aproximation for U- and V-statistics of a stationary absolutely regular sequence”, Siberian Electr. Math. Rep., 17 (2020), 672–682.10.33048/semi.2020.17.045Suche in Google Scholar

[20] Ross N., “Fundamentals of Stein’s method”, Probability Surveys, 8 (2011), 210–293.10.1214/11-PS182Suche in Google Scholar