Geodesic
Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 250-266 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We examine certain questions, related to the convergence rate in the so-called “precise asymptotics”, when a limiting law is stable (including the normal one). In particular, the results obtained in Gut and Steinebach, (Ann. Univ. Sci. Budapest. Sect. Comput. 39:95–110, 2013) are generalized and refined. 
@article{ZNSL_2020_495_a14,
     author = {L. V. Rozovsky},
     title = {Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {250--266},
     year = {2020},
     volume = {495},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a14/}
}
TY  - JOUR
AU  - L. V. Rozovsky
TI  - Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 250
EP  - 266
VL  - 495
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a14/
LA  - ru
ID  - ZNSL_2020_495_a14
ER  - 
%0 Journal Article
%A L. V. Rozovsky
%T Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 250-266
%V 495
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a14/
%G ru
%F ZNSL_2020_495_a14
L. V. Rozovsky. Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of normal attraction of a stable distribution. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 29, Tome 495 (2020), pp. 250-266. http://geodesic.mathdoc.fr/item/ZNSL_2020_495_a14/

[1] P. Hall, “Two-sided bounds on the rate of convergence to a stable law”, Z. Wahrscheinlichkeitstheorie verw. Geb., 57 (1981), 349–364 | DOI | MR | Zbl

[2] A. Gut, J. Steinebach, “Convergence rates in precise asymptotics II”, Ann. Univ. Sci. Budapest. Sect. Comput., 39 (2013), 95–110 | MR | Zbl

[3] A. Gut, J. Steinebach, “Precise asymptotics – a general approach”, Acta Math. Hung., 138:4 (2013), 365–385 | DOI | MR | Zbl

[4] L. T. Kong, “Convergence rate in precise asymptotics for the law of the iterated logarithm”, Lith. Math. J., 56:3 (2016), 318–324 | DOI | MR | Zbl

[5] L. T. Kong, H. S. Dai, “Convergence rate in precise asymptotics for Davis law of large numbers”, Stat. Probab. Lett., 119:10 (2016), 295–300 | DOI | MR | Zbl

[6] Y. Zhang, “A note on the convergence rates in precise asymptotics”, J. Ineq. Appl., 15 (2019) | MR

[7] L. V. Rozovsky, “Some limit theorems for large deviations of sums of independent random variables with a common distribution function from the domain of attraction of the normal law”, J. Math. Sci., 127 (2005), 1767–1783 | DOI | MR | Zbl

[8] V. M. Zolotarev, Odnomernye ustoichivye raspredeleniya, Nauka, M., 1983, 304 pp. | MR

[9] F. N. Galstyan, “O skorosti skhodimosti v tsentralnoi predelnoi teoreme”, Teoriya veroyatnostei i matematicheskaya statistika, 5, Izd-vo Kiev. univ., 1971, 14–26 | MR

[10] V. V. Petrov, Summy nezavisimykh sluchainykh velichin, Nauka, M., 1972, 416 pp.