Geodesic
On bounds for characteristic functions of the powers of asymptotically normal random variables
Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 122-144

Voir la notice de l'article provenant de la source Math-Net.Ru

We obtain upper bounds for the absolute values of the characteristic functions of the $k$th powers of asymptotically normal random variables. Estimates are proved for the case when asymptotically normal random variables are normalized sums of independent identically distributed summands with a “regular” distribution. Possible generalizations are considered. The estimates extend the results of previous studies, where for the distributions of the summands, the presence of either a discrete or an absolutely continuous component was required. The proofs of the bounds are based on the stochastic generalization of the I. M. Vinogradov mean value theorem, which is also obtained in the present paper.
Keywords: powers of random variables, bounds for characteristic functions, the Vinogradov mean value theorem, stochastic generalization. 
@article{TVP_2017_62_1_a7,
     author = {Yu. V. Prokhorov and F. G\"otze and V. V. Ulyanov},
     title = {On bounds for characteristic functions of the powers of asymptotically normal random variables},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {122--144},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a7/}
}
TY  - JOUR
AU  - Yu. V. Prokhorov
AU  - F. Götze
AU  - V. V. Ulyanov
TI  - On bounds for characteristic functions of the powers of asymptotically normal random variables
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2017
SP  - 122
EP  - 144
VL  - 62
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a7/
LA  - ru
ID  - TVP_2017_62_1_a7
ER  - 
%0 Journal Article
%A Yu. V. Prokhorov
%A F. Götze
%A V. V. Ulyanov
%T On bounds for characteristic functions of the powers of asymptotically normal random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2017
%P 122-144
%V 62
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a7/
%G ru
%F TVP_2017_62_1_a7
Yu. V. Prokhorov; F. Götze; V. V. Ulyanov. On bounds for characteristic functions of the powers of asymptotically normal random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 62 (2017) no. 1, pp. 122-144. http://geodesic.mathdoc.fr/item/TVP_2017_62_1_a7/