On the upper bound in the large deviation principle for sums of random vectors
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 twodimensional random walk, this bound holds without any additional assumptions.
Keywordslarge deviation principle upper bound in the large deviation principle deviation function Cramér’s condition
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