Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 51-63
Citer cet article
A. V. Nagaev. Integral limit theorems taking into account large deviations when Cramer's condition does not hold. I. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 1, pp. 51-63. http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a5/
@article{TVP_1969_14_1_a5,
author = {A. V. Nagaev},
title = {Integral limit theorems taking into account large deviations when {Cramer's} condition does not {hold.~I}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {51--63},
year = {1969},
volume = {14},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a5/}
}
TY - JOUR
AU - A. V. Nagaev
TI - Integral limit theorems taking into account large deviations when Cramer's condition does not hold. I
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1969
SP - 51
EP - 63
VL - 14
IS - 1
UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a5/
LA - ru
ID - TVP_1969_14_1_a5
ER -
%0 Journal Article
%A A. V. Nagaev
%T Integral limit theorems taking into account large deviations when Cramer's condition does not hold. I
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1969
%P 51-63
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1969_14_1_a5/
%G ru
%F TVP_1969_14_1_a5
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 $x>\sqrt n$.
