Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 520-527
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V. A. Egorov. On the strong law of large numbers and the law of the iterated logarithm for a sequence of independent random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 3, pp. 520-527. http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a7/
@article{TVP_1970_15_3_a7,
author = {V. A. Egorov},
title = {On the strong law of large numbers and the law of the iterated logarithm for a~sequence of independent random variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {520--527},
year = {1970},
volume = {15},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a7/}
}
TY - JOUR
AU - V. A. Egorov
TI - On the strong law of large numbers and the law of the iterated logarithm for a sequence of independent random variables
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1970
SP - 520
EP - 527
VL - 15
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a7/
LA - ru
ID - TVP_1970_15_3_a7
ER -
%0 Journal Article
%A V. A. Egorov
%T On the strong law of large numbers and the law of the iterated logarithm for a sequence of independent random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1970
%P 520-527
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a7/
%G ru
%F TVP_1970_15_3_a7
Let $\{X_n\}$ be a sequence of independent random variables with zero means and finite variances, $\{b_n\}$ be an increasing sequence of positive numbers, $b_n\to\infty$, $X_n=o(b_n)$ a.s. Some new conditions are found which are sufficient for the equality $\sum_{j=1}^nX_j=o(b_n)$ a.s. These conditions are expressed in terms of second moments. New sufficient conditions for the law of the iterated logarithm are also obtained.
