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This article is cited in 12 papers
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 $x>\sqrt n$.
Received: 10.10.1967
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
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{http://www.zentralblatt-math.org/zmath/search/?an=Zbl 0196.21002|Zbl 0172.21901}
\transl
\jour Theory Probab. Appl.
\yr 1969
\vol 14
\issue 1
\pages 51--64
\crossref{http://dx.doi.org/10.1137/1114006}
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Theory of Probability and its Applications, 1969, 14:1, 51–64
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