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Mat. Tr., 2013, Volume 16, Number 1, Pages 121–140 (Mi mt252)  

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

A. A. Mogul'skiĭab

a 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.

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

Bibliographic databases:

UDC: 519.21
Received: 29.05.2012

Citation: A. A. Mogul'skiǐ, “On the upper bound in the large deviation principle for sums of random vectors”, Mat. Tr., 16:1 (2013), 121–140; Siberian Adv. Math., 24:2 (2014), 140–152

Citation in format AMSBIB
\Bibitem{Mog13}
\by A.~A.~Mogul'ski{\v\i}
\paper On the upper bound in the large deviation principle for sums of random vectors
\jour Mat. Tr.
\yr 2013
\vol 16
\issue 1
\pages 121--140
\mathnet{http://mi.mathnet.ru/mt252}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3156676}
\elib{https://elibrary.ru/item.asp?id=19000375}
\transl
\jour Siberian Adv. Math.
\yr 2014
\vol 24
\issue 2
\pages 140--152
\crossref{https://doi.org/10.3103/S1055134414020047}


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