Geodesic
Asymptotic expansions of the distribution functions of the sums of independent equally distributed lattice random vectors
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 499-507

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Let $$ S_n=\frac1{\sqrt n}\sum_{j=1}^n(\xi_j-\mathbf M\xi_j) $$ be the normalized sum of independent equally distributed lattice random vectors $\xi_1,\xi_2,\dots,\xi_n$. In this paper, asymptotic expansions of the probability function $P_n(A)$, $A$ being a Borel set, of $S_n$ are considered. 
@article{TVP_1969_14_3_a8,
     author = {A. Bikelis},
     title = {Asymptotic expansions of the distribution functions of the sums of independent equally distributed lattice random vectors},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {499--507},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a8/}
}
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A. Bikelis. Asymptotic expansions of the distribution functions of the sums of independent equally distributed lattice random vectors. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 3, pp. 499-507. http://geodesic.mathdoc.fr/item/TVP_1969_14_3_a8/