Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 393-395
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S. V. Nagaev; M. S. Èppel'. On a local limit theorem for the sums of independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 2, pp. 393-395. http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a14/
@article{TVP_1976_21_2_a14,
author = {S. V. Nagaev and M. S. \`Eppel'},
title = {On a~local limit theorem for the sums of independent random variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {393--395},
year = {1976},
volume = {21},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a14/}
}
TY - JOUR
AU - S. V. Nagaev
AU - M. S. Èppel'
TI - On a local limit theorem for the sums of independent random variables
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1976
SP - 393
EP - 395
VL - 21
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a14/
LA - ru
ID - TVP_1976_21_2_a14
ER -
%0 Journal Article
%A S. V. Nagaev
%A M. S. Èppel'
%T On a local limit theorem for the sums of independent random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1976
%P 393-395
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1976_21_2_a14/
%G ru
%F TVP_1976_21_2_a14
Let $X_i$, $i\to\overline{1,\infty}$, be independent identically distributed random variables with $\mathbf EX_i=0$, $\mathbf DX_i=\sigma^2<\infty$, and let $\displaystyle S_n=\sum_1^nX_i$, $\displaystyle\overline S_n=\max_{1\le k\le n}S_k$. A local limit theorem for the probabilities $\mathbf P(\overline S_n=x)$ is formulated in the case when $x=o(\sqrt n)$. This result complements the local limit theorem proved in [1]
