Siberian Advances in Mathematics

, Volume 24, Issue 2, pp 140–152 | Cite as

On the upper bound in the large deviation principle for sums of random vectors

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Abstract

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.

Keywords

large deviation principle upper bound in the large deviation principle deviation function Cramér’s condition 

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Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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