Geodesic
Limit theorems for large deviations of sums of independent not necessarily identically distributed lattice random vectors
Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 47-64.

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We estimate the probabilities of large deviations of sums of independent lattice random vectors which take values from the $k$-dimensional Euclidean space and may be not identically distributed. Under the hypothesis that the Cramér condition in the lattice case is satisfied, we formulate a local limit theorem and prove an integral limit theorem for some class of convex Borel sets. 
@article{DM_1996_8_3_a4,
     author = {K. V. Petrovskii},
     title = {Limit theorems for large deviations of sums of independent not necessarily identically distributed lattice random vectors},
     journal = {Diskretnaya Matematika},
     pages = {47--64},
     publisher = {mathdoc},
     volume = {8},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1996_8_3_a4/}
}
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K. V. Petrovskii. Limit theorems for large deviations of sums of independent not necessarily identically distributed lattice random vectors. Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 47-64. http://geodesic.mathdoc.fr/item/DM_1996_8_3_a4/