Diskretnaya Matematika, Tome 8 (1996) no. 3, pp. 47-64
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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/
@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},
year = {1996},
volume = {8},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_1996_8_3_a4/}
}
TY - JOUR
AU - K. V. Petrovskii
TI - Limit theorems for large deviations of sums of independent not necessarily identically distributed lattice random vectors
JO - Diskretnaya Matematika
PY - 1996
SP - 47
EP - 64
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/item/DM_1996_8_3_a4/
LA - ru
ID - DM_1996_8_3_a4
ER -
%0 Journal Article
%A K. V. Petrovskii
%T Limit theorems for large deviations of sums of independent not necessarily identically distributed lattice random vectors
%J Diskretnaya Matematika
%D 1996
%P 47-64
%V 8
%N 3
%U http://geodesic.mathdoc.fr/item/DM_1996_8_3_a4/
%G ru
%F DM_1996_8_3_a4
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.
