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 Teor. Veroyatnost. i Primenen., 1969, Volume 14, Issue 1, Pages 51–63 (Mi tvp1116)

Integral limit theorems taking into account large deviations when Cramer's condition does not hold. I

A. V. Nagaev

Tashkent

Abstract: Let $\xi_1,…,\xi_n$ be a sequence of independent equally distributed random variables with $\mathbf M\xi_n=0$. Throughout the paper it is supposed that the density function $p(x)$ of $\xi^n$ has the property
$$p(x)\sim e^{-|x|^{1-\varepsilon}},\quad0<\varepsilon<1,\quad|x|\to\infty.$$
The problem we deal with is to describe the behaviour of the probability $\mathbf P\{\xi_1+…+\xi_n>x\}$ when $x$ tends to infinity so that $x>\sqrt n$.

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English version:
Theory of Probability and its Applications, 1969, 14:1, 51–64

Bibliographic databases:

Citation: A. V. Nagaev, “Integral limit theorems taking into account large deviations when Cramer's condition does not hold. I”, Teor. Veroyatnost. i Primenen., 14:1 (1969), 51–63; Theory Probab. Appl., 14:1 (1969), 51–64

Citation in format AMSBIB
\Bibitem{Nag69} \by A.~V.~Nagaev \paper Integral limit theorems taking into account large deviations when Cramer's condition does not hold.~I \jour Teor. Veroyatnost. i Primenen. \yr 1969 \vol 14 \issue 1 \pages 51--63 \mathnet{http://mi.mathnet.ru/tvp1116} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=247651} \zmath{https://zbmath.org/?q=an:0196.21002|0172.21901} \transl \jour Theory Probab. Appl. \yr 1969 \vol 14 \issue 1 \pages 51--64 \crossref{https://doi.org/10.1137/1114006} 

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