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Teoriya Veroyatnostei i ee Primeneniya, 1969, Volume 14, Issue 1, Pages 51–63
(Mi tvp1116)
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This article is cited in 106 scientific papers (total in 106 papers)
Integral limit theorems taking into account large deviations when Cramer's condition does not hold. I
A. V. Nagaev Tashkent
Abstract:
Let $\xi_1,\dots,\xi_n$ 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 $\mathbf P\{\xi_1+\dots+\xi_n>x\}$ 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; Theory Probab. Appl., 14:1 (1969), 51–64
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