Geodesic
Multidimensional limit theorems for large deviations
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 1, pp. 40-57 
L. V. Osipov. Multidimensional limit theorems for large deviations. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 1, pp. 40-57. http://geodesic.mathdoc.fr/item/TVP_1975_20_1_a3/
@article{TVP_1975_20_1_a3,
     author = {L. V. Osipov},
     title = {Multidimensional limit theorems for large deviations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {40--57},
     year = {1975},
     volume = {20},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_1_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $S_n=X^{(1)}+\dots+X^{(n)}$ be a sum of independent identically distributed random vectors in $R^k$ and let $\Phi$ be the standard normal distribution in $R^k$. Conditions upon distribution of $X^{(1)}$ are given under which $$ \mathbf P\{S_n/\sqrt n\in A_n\}=\Phi(A_n)(1+o(1)),\quad n\to\infty, $$ uniformly in sequences of Borel sets $\{A_n\}$ such that $\Phi(A_n)\ge\Phi(x\colon|x|>\Lambda(n))$ where $\Lambda(z)\uparrow\infty$ is a function satisfying condition (8). In Theorems 1 and 2, we consider the case $\Lambda(z)=bz^\alpha$, $b>0$, $0<\alpha<1/2$.