@article{TVP_2010_55_3_a9,
author = {V. Yu. Korolev and I. G. Shevtsova},
title = {A new moment estimate of the convergence rate in the {Lyapunov} theorem},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {577--582},
year = {2010},
volume = {55},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a9/}
}
V. Yu. Korolev; I. G. Shevtsova. A new moment estimate of the convergence rate in the Lyapunov theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 3, pp. 577-582. http://geodesic.mathdoc.fr/item/TVP_2010_55_3_a9/
[1] Bkhattachariya R. N., Ranga Rao R., Approksimatsiya normalnym raspredeleniem, Nauka, M., 1982, 286 pp.
[2] Korolev V. Yu., Shevtsova I. G., “O verkhnei otsenke absolyutnoi postoyannoi v neravenstve Berri–Esseena”, Teoriya veroyatn. i ee primen., 54:4 (2009), 671–695
[3] Korolev V. Yu., Shevtsova I. G., “Utochnenie neravenstva Berri–Esseena”, Dokl. RAN, 430:6 (2010), 738–742 | MR | Zbl
[4] Korolev V. Yu., Shevtsova I. G., “Utochnenie neravenstva Berri–Esseena s prilozheniyami k puassonovskim i smeshannym puassonovskim sluchainym summam”, Obozrenie prikl. i promyshl. matem., 17:1 (2010), 25–56
[5] Paulauskas V. I., “Ob odnom usilenii teoremy Lyapunova”, Litov. matem. sb., 9:2 (1969), 173–179
[6] Tyurin I. S., “O tochnosti gaussovskoi approksimatsii”, Dokl. RAN, 429:3 (2009), 312–316 | MR | Zbl
[7] Tyurin I. S., “Utochnenie verkhnikh otsenok konstant v teoreme Lyapunova”, Uspekhi matem. nauk, 65:3(393) (2010), 201–202 | MR
[8] Shevtsova I. G., “Nizhnyaya asimptoticheski pravilnaya postoyannaya v tsentralnoi predelnoi teoreme”, Dokl. RAN, 430:4 (2010), 466–469 | MR | Zbl
[9] Shevtsova I. G., “Utochnenie otsenok skorosti skhodimosti v teoreme Lyapunova”, Dokl. RAN, 2010 (to appear)
[10] Berry A. C., “The accuracy of the Gaussian approximation to the sum of independent variables”, Trans. Amer. Math. Soc., 49 (1941), 122–136 | MR
[11] Esseen C.-G., “On the Liapunoff limit of error in the theory of probability”, Ark. Mat. Astron. Fys., A28:9 (1942), 1–19 ; | MR | Zbl | DOI
[12] Esseen C.-G., “A moment inequality with an application to the central limit theorem”, Skand. Aktuarietidskr., 39 (1956), 160–170 | MR
[13] Korolev V. Yu., Shevtsova I. G., “An improvement of the Berry–Esseen inequality with applications to Poisson and mixed Poisson random sums”, Scand. Actuar. J., 2010 (to appear) | MR
[14] Prawitz H., “Limits for a distribution, if the characteristic function is given in a finite domain”, Scand. Aktuarietidskr., 1972 (1972), 138–154 | MR
[15] Prawitz H., “Weitere Ungleichungen für den absoluten Betrag einer charakteristischen Funktion”, Scand. Actuar. J., 1975 (1975), 21–28. | MR | Zbl
[16] Prawitz H., “On the remainder in the central limit theorem”, Scand. Actuar. J., 1975:3 (1975), 145–156 | MR | Zbl
[17] Wallace D. L., A corrected computation of Berry's bound for the central limit theorem error, Stat. Res. Cent., University of Chicago, Chicago, 1959
[18] Zahl S., “Bounds for the central limit theorem error”, SIAM J. Appl. Math., 14:6 (1966), 1225–1245 | DOI | MR | Zbl