Geodesic
An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses
Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 627-640

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

Let $X_1,\dots,X_n$ ($n\ge1$) be independent random vectors in $R_d$, $b$b be a vector in $R_d$. For an arbitrary Borel set $A\subset R_d$ we set \begin{gather*} P_n(A)=P\{X_1+\dots+X_n-b\in A\}, \\ \Delta_n(A)=|P_n(a)-\Phi(A)|, \end{gather*} where $\Phi(A)$ is the probability function of a standard normal vector in $R_d$. In this note are obtained estimates for $\Delta_n(A)$, where $A$ belongs to the class of convex Borel sets in $R_d$. 
@article{MZM_1978_23_4_a14,
     author = {L. V. Rozovskii},
     title = {An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses},
     journal = {Matemati\v{c}eskie zametki},
     pages = {627--640},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/}
}
TY  - JOUR
AU  - L. V. Rozovskii
TI  - An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses
JO  - Matematičeskie zametki
PY  - 1978
SP  - 627
EP  - 640
VL  - 23
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/
LA  - ru
ID  - MZM_1978_23_4_a14
ER  - 
%0 Journal Article
%A L. V. Rozovskii
%T An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses
%J Matematičeskie zametki
%D 1978
%P 627-640
%V 23
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/
%G ru
%F MZM_1978_23_4_a14
L. V. Rozovskii. An estimate of the speed of convergence in the multidmensional central limit theorem without moment hypotheses. Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 627-640. http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a14/