@article{TVP_2010_55_3_a3,
author = {N. K. Bakirov and G. J. Szekely},
title = {Brownian covariance and central limit theorem for stationary sequences},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {462--488},
year = {2010},
volume = {55},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a3/}
}
N. K. Bakirov; G. J. Szekely. Brownian covariance and central limit theorem for stationary sequences. Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 3, pp. 462-488. http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a3/
[1] Bradley R. C., “Central limit theorem under weak dependence”, J. Multivariate Anal., 11:1 (1981), 1–16 | DOI | MR | Zbl
[2] Bradley R. C., “A central limit theorem for stationary $\rho$-mixing sequences with infinite variance”, Ann. Probab., 16:1 (1988), 313–332 | DOI | MR | Zbl
[3] Bradley R. C., Introduction to Strong Mixing Condition, v. 1–3, Kendrick Press, Heber City, 2007, 539 pp. ; 553 pp.; 597 pp. | MR
[4] Dedecker J., Merlevède F., “Necessary and sufficient conditions for the conditional central limit theorem”, Ann. Probab., 30:3 (2002), 1044–1081 | DOI | MR | Zbl
[5] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984, 752 pp. | MR
[6] Gordin M. I., “O tsentralnoi predelnoi teoreme dlya statsionarnykh protsessov”, Dokl. AN SSSR, 188:4 (1969), 739–741 | MR | Zbl
[7] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Nauka, M., 1971, 1108 pp.
[8] Herbin E., Merzbach E., “The multiparameter fractional Brownian motion”, Math Everywhere, Springer, Berlin, 2007, 93–101 | MR | Zbl
[9] Herrndorf N., “Stationary strongly mixing sequences not satisfying the central limit theorem”, Ann. Probab., 11:3 (1983), 809–813 | DOI | MR | Zbl
[10] Hoeffding W., “A nonparametric test of independence”, Ann. Math. Statist., 19 (1948), 546–557 | DOI | MR | Zbl
[11] Ibragimov I. A., “Nekotorye predelnye teoremy dlya statsionarnykh protsessov”, Teoriya veroyatn. i ee primen., 7:4 (1962), 349–382 | Zbl
[12] Ibragimov I. A., Linnik Yu. V., Nezavisimye i statsionarno svyazannye velichiny, Nauka, M., 1965, 524 pp.
[13] Landau H. J., Shepp L. A., “On the supremum of a Gaussian process”, Sankyā Ser. A, 32 (1970), 369–378 | MR | Zbl
[14] Merlevède F., Peligrad M., “The functional central limit theorem under the strong mixing condition”, Ann. Probab., 28:3 (2000), 1336–1352 | DOI | MR | Zbl
[15] Peligrad M., “On the central limit theorem for $\rho$-mixing sequences of random variables”, Ann. Probab., 15:4 (1987), 1387–1394 | DOI | MR | Zbl
[16] Peligrad M., Utev S., “Central limit theorem for stationary linear processes”, Ann. Probab., 34:4 (2006), 1608–1622 | DOI | MR | Zbl
[17] Rosenblatt M., “A central limit theorem and a strong mixing condition”, Proc. Natl. Acad. Sci. USA, 42 (1956), 43–47 | DOI | MR | Zbl
[18] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985, 141 pp. | MR | Zbl
[19] Székely G. J., Rizzo M. L., Bakirov N. K., “Measuring and testing independence by correlation of distances”, Ann. Statist., 35:6 (2007), 2769–2794 | DOI | MR | Zbl
[20] Talagrand M., “Small tails for the supremum of a Gaussian process”, Ann. Inst. H. Poincaré, 24:2 (1988), 307–315 | MR | Zbl
[21] Wu W. B., Woodroofe M., “Martingale approximations for sums of stationary processes”, Ann. Probab., 32:2 (2004), 1674–1690 | DOI | MR | Zbl