Geodesic
Estimate of the rate of convergence of probability distributions to a uniform distribution
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 780-787

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

The paper considers sequences of random vectors in the Euclidean space $\mathbf{R}^s (s\ge2)$: $X_1,X_2,\dots,X_n,\dots,X_n=(X_{n1},\dots,X_{ns})$, $0\le X_{nj}\le 1$, $j=1,\ldots,s$. A deviation of a distribution of the random vectors $X_n$ from a uniform distribution on a cube $[0,1]^s$ is evaluated in terms of mathematical expectations $\mathbf{E} e^{2\pi i(m,X_n)}$, where $m$ is a vector with integer-valued coordinates. If they decrease rapidly enough as $n\to\infty$ for any convex domain $D\subset[0,1]^s$, the value $|\mathbf{P}\{X_n\in D\}-\mathrm{vol}_s(D)|$ decreases as some positive order of $1/n$. This work is a generalization of [A. Ya. Kuznetsova and A. A. Kulikova, Moscow Univ. Comput. Math. Cybernet., 2002, no. 3, pp. 35–43], in which $s=1$ was assumed.
Mots-clés : convergence of distributions, summation Poisson formula.
Keywords: uniform distribution 
@article{TVP_2002_47_4_a10,
     author = {A. A. Kulikova},
     title = {Estimate of the rate of convergence of probability distributions to a uniform distribution},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {780--787},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a10/}
}
TY  - JOUR
AU  - A. A. Kulikova
TI  - Estimate of the rate of convergence of probability distributions to a uniform distribution
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2002
SP  - 780
EP  - 787
VL  - 47
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a10/
LA  - ru
ID  - TVP_2002_47_4_a10
ER  - 
%0 Journal Article
%A A. A. Kulikova
%T Estimate of the rate of convergence of probability distributions to a uniform distribution
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2002
%P 780-787
%V 47
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a10/
%G ru
%F TVP_2002_47_4_a10
A. A. Kulikova. Estimate of the rate of convergence of probability distributions to a uniform distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 4, pp. 780-787. http://geodesic.mathdoc.fr/item/TVP_2002_47_4_a10/