Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 3, pp. 566-568
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A. S. Mal'kov; V. V. Ul'yanov. On the non-uniform estimate of the rate of convergence in the local limit theorem in the case of a stable limit distribution. Teoriâ veroâtnostej i ee primeneniâ, Tome 27 (1982) no. 3, pp. 566-568. http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a13/
@article{TVP_1982_27_3_a13,
author = {A. S. Mal'kov and V. V. Ul'yanov},
title = {On the non-uniform estimate of the rate of convergence in the local limit theorem in the case of a~stable limit distribution},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {566--568},
year = {1982},
volume = {27},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a13/}
}
TY - JOUR
AU - A. S. Mal'kov
AU - V. V. Ul'yanov
TI - On the non-uniform estimate of the rate of convergence in the local limit theorem in the case of a stable limit distribution
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1982
SP - 566
EP - 568
VL - 27
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a13/
LA - ru
ID - TVP_1982_27_3_a13
ER -
%0 Journal Article
%A A. S. Mal'kov
%A V. V. Ul'yanov
%T On the non-uniform estimate of the rate of convergence in the local limit theorem in the case of a stable limit distribution
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1982
%P 566-568
%V 27
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1982_27_3_a13/
%G ru
%F TVP_1982_27_3_a13
Let $p_n(x)$ be a probability density function of normalized and centered sum of $n$ i. i. d. random variables belonging to the domain of attraction of the stable distribution $G$ of index $\alpha$, $0<\alpha\le 2$, $\alpha\ne 1$. Let $p(x)$ be a probability density function of $G$. It is proved that under certain conditions the relation $$ \lim_{n\to\infty}|x|^\delta|p_n(x)-p(x)|=0,\qquad 0\le\delta<\alpha\ne 1, $$ holds uniformly in $x$, $-\infty.
