Geodesic
On concentration of distributions of sums of independent random vectors on bounded sets
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 882-891

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Bounds are obtained for the concentration function $$ Q_n (A) =\sup_{x\in\mathbf{R}^k}{\mathbf P}(S_n \in A + x) $$ of sums $S_n=X_1+\cdots+X_n $ of independent random vectors $X_1,\ldots,X_n$ with values in the $k$-dimensional Euclidean space $\mathbf{R}^k$ on bounded Borel sets $A$ in $\mathbf{R}^k$.
Keywords: concentration function, Esseen inequality, Enger inequality, spherical and non-spherical concentration functions. 
@article{TVP_1993_38_4_a11,
     author = {Yu. V. Larin},
     title = {On concentration of distributions of sums of independent random vectors on bounded sets},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {882--891},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a11/}
}
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Yu. V. Larin. On concentration of distributions of sums of independent random vectors on bounded sets. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 882-891. http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a11/