Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 2, pp. 364-366
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A. I. Martikaǐnen. A converse to the law of the iterated logarithm for random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 25 (1980) no. 2, pp. 364-366. http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a11/
@article{TVP_1980_25_2_a11,
author = {A. I. Martikaǐnen},
title = {A converse to the law of the iterated logarithm for random walk},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {364--366},
year = {1980},
volume = {25},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a11/}
}
TY - JOUR
AU - A. I. Martikaǐnen
TI - A converse to the law of the iterated logarithm for random walk
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1980
SP - 364
EP - 366
VL - 25
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a11/
LA - ru
ID - TVP_1980_25_2_a11
ER -
%0 Journal Article
%A A. I. Martikaǐnen
%T A converse to the law of the iterated logarithm for random walk
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1980
%P 364-366
%V 25
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1980_25_2_a11/
%G ru
%F TVP_1980_25_2_a11
Let $\{S_n\}$ be a random walk with independent increments. Then $\mathbf{E}S_1=0$, $\mathbf{E}S_1^2=1$ iff $$ \limsup_{n\to\infty}\frac{S_n}{\sqrt{2n\log\log n}}=1\qquad\text{almost surely.} $$
