Geodesic
On the upper bound in the large deviation principle for sums of random vectors
Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 121-140.

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We consider the random walk generated by a sequence of independent identically distributed random vectors. The known upper bound for normalized sums in the large deviation principle was established under the assumption that the Laplace–Stieltjes transform of the distribution of the walk jumps exists in a neighborhood of zero. In the present article, we prove that, for a two-dimensional random walk, this bound holds without any additional assumptions. 
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A. A. Mogul'skiǐ. On the upper bound in the large deviation principle for sums of random vectors. Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 121-140. http://geodesic.mathdoc.fr/item/MT_2013_16_1_a6/

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