Growth of sums of pairwise independent random variables with infinite means
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 382-385
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It is proved that $\textbf P\{|S_n|>a_n$ infinitely often$\}=0$ or $1$ if the series $\sum_{n=1}^{\infty}\textbf P\{|X_n|>a_n\}$ is convergent or nonconvergent, where $S_n=X_1+\dots+X_n$ is a sum of identically distributed pairwise independent random variables with infinite expectations, $a_n>0$, for some $m$ a sequence $\{a_n\}_{n\ge m}$ strictly increasing and convex.
Keywords:
random variable, pairwise independence.
@article{TVP_2006_51_2_a7,
author = {V. M. Kruglov},
title = {Growth of sums of pairwise independent random variables with infinite means},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {382--385},
publisher = {mathdoc},
volume = {51},
number = {2},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a7/}
}
V. M. Kruglov. Growth of sums of pairwise independent random variables with infinite means. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 2, pp. 382-385. http://geodesic.mathdoc.fr/item/TVP_2006_51_2_a7/