Geodesic
Upper bounds for the concentration function in a~Hilbert space
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 335-349

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

New bounds (analogous to the bounds obtained by Kolmogorov, Rogozin and Esseen) are derived for the concentration function of the sums of independent random variables with values in a Hilbert space. In particular, the absolute constants used in the estimates don't depend on the dimension in the finite-dimensional space. Further, some limit theorems for the concentration function and some estimates for the concentration functions of infinitely divisible distributions are given. 
@article{TVP_1981_26_2_a6,
     author = {G. Siegel},
     title = {Upper bounds for the concentration function in {a~Hilbert} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {335--349},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a6/}
}
TY  - JOUR
AU  - G. Siegel
TI  - Upper bounds for the concentration function in a~Hilbert space
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1981
SP  - 335
EP  - 349
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a6/
LA  - ru
ID  - TVP_1981_26_2_a6
ER  - 
%0 Journal Article
%A G. Siegel
%T Upper bounds for the concentration function in a~Hilbert space
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1981
%P 335-349
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a6/
%G ru
%F TVP_1981_26_2_a6
G. Siegel. Upper bounds for the concentration function in a~Hilbert space. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 335-349. http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a6/