Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 203-216
Citer cet article
A. V. Nagaev. Integral limit theorems taking into account large deviations when Cramér's condition does not hold. II. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 2, pp. 203-216. http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a1/
@article{TVP_1969_14_2_a1,
author = {A. V. Nagaev},
title = {Integral limit theorems taking into account large deviations when {Cram\'er's} condition does not {hold.~II}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {203--216},
year = {1969},
volume = {14},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a1/}
}
TY - JOUR
AU - A. V. Nagaev
TI - Integral limit theorems taking into account large deviations when Cramér's condition does not hold. II
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1969
SP - 203
EP - 216
VL - 14
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a1/
LA - ru
ID - TVP_1969_14_2_a1
ER -
%0 Journal Article
%A A. V. Nagaev
%T Integral limit theorems taking into account large deviations when Cramér's condition does not hold. II
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1969
%P 203-216
%V 14
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1969_14_2_a1/
%G ru
%F TVP_1969_14_2_a1
Let $\xi_1,\dots\xi_n,\dots$ be a sequence of independent equally distributed random variables and $\mathbf M\xi_n=0$. The density function $p(x)$ of $\xi_n$ being assumed to satisfy the condition $$ p(x)\sim e^{-|x|^{1-\varepsilon}},\quad0<\varepsilon<1,\quad\text{as }|x|\to\infty, $$ the behaviour of the probability $\mathbf P\{\xi_i+\dots+\xi_n>x\}$ is studied when $n$ and $x$ tend to infinity so that $x>\sqrt n$.
