This article is cited in 3 papers

Short Communications

Growth of sums of pairwise independent random variables with infinite means

V. M. Kruglov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: 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.

Received: 21.06.2004

DOI: 10.4213/tvp60

 English version: Theory of Probability and its Applications, 2007, 51:2, 359–362

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