Geodesic
The probabilities of large deriations on Borel sets
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VIII, Tome 130 (1983), pp. 157-166

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

Accuracy of the approximation of the probability $P_n(A_n)=\mathbf P(\frac1{\sqrt n}(X_1+\dots+X_n)\in A_n)$ by $\Phi(A_n)$ is studied for Borel sets $A_n$, $\Phi(A_n)\to0$. The necessary and sufficient conditions are obtained for $P_n(A_n)=\Phi(A_n)(1+O(\ae(\sqrt n)))$ uniformly in all sequences $\{A_n\}$ such that $\Phi(A_n)\geqslant\Phi(x:|x|>\bar\Lambda(\sqrt n))$. Here $\ae(z)\downarrow0$, $\bar\Lambda(z)\uparrow\infty$ are functions satisfying some conditions. 
@article{ZNSL_1983_130_a16,
     author = {L. V. Rozovskii},
     title = {The probabilities of large deriations on {Borel} sets},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {157--166},
     publisher = {mathdoc},
     volume = {130},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1983_130_a16/}
}
TY  - JOUR
AU  - L. V. Rozovskii
TI  - The probabilities of large deriations on Borel sets
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1983
SP  - 157
EP  - 166
VL  - 130
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1983_130_a16/
LA  - ru
ID  - ZNSL_1983_130_a16
ER  - 
%0 Journal Article
%A L. V. Rozovskii
%T The probabilities of large deriations on Borel sets
%J Zapiski Nauchnykh Seminarov POMI
%D 1983
%P 157-166
%V 130
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1983_130_a16/
%G ru
%F ZNSL_1983_130_a16
L. V. Rozovskii. The probabilities of large deriations on Borel sets. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VIII, Tome 130 (1983), pp. 157-166. http://geodesic.mathdoc.fr/item/ZNSL_1983_130_a16/