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
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
@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},
publisher = {mathdoc},
volume = {15},
number = {3},
year = {1970},
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 PB - mathdoc 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 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1970_15_3_a7/ %G ru %F TVP_1970_15_3_a7
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/