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

A. A. Mogul'skiĭ<sup>ab

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

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 two-dimensional random walk, this bound holds without any additional assumptions.

Key words: large deviation principle, upper bound in the large deviation principle, deviation function, Cramér's condition.

UDC: 519.21

Received: 29.05.2012

 English version: Siberian Advances in Mathematics, 2014, 24:2, 140–152

Bibliographic databases:

• 
•