Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 637-645
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A. V. Nagaev. On asymmetric large deviations problem in the case of the stable limit law. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 4, pp. 637-645. http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a1/
@article{TVP_1983_28_4_a1,
author = {A. V. Nagaev},
title = {On asymmetric large deviations problem in the case of the stable limit law},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {637--645},
year = {1983},
volume = {28},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a1/}
}
TY - JOUR
AU - A. V. Nagaev
TI - On asymmetric large deviations problem in the case of the stable limit law
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1983
SP - 637
EP - 645
VL - 28
IS - 4
UR - http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a1/
LA - ru
ID - TVP_1983_28_4_a1
ER -
%0 Journal Article
%A A. V. Nagaev
%T On asymmetric large deviations problem in the case of the stable limit law
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1983
%P 637-645
%V 28
%N 4
%U http://geodesic.mathdoc.fr/item/TVP_1983_28_4_a1/
%G ru
%F TVP_1983_28_4_a1
Let $\xi_j$ be i. i. d. random variables such that for $x\ge x_0$$$ \mathbf P\{\xi_1>x\}=x^{-\alpha}l(x),\quad\mathbf P\{\xi_1<-x\}=x^{-\beta}m(x), $$ where $0<\alpha<1$, $\beta>\alpha$ and the functions $l(x)$ and $m(x)$ vary slowly as $x\to\infty$. We study the asymptotic behaviour of $$ \mathbf P\{\xi_1+\dots+\xi_n<x\}\quad\text{for}\ x=0\ (\inf\{y:\ ny^{-\alpha}l(y)\le 1\}). $$
