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Teoriya Veroyatnostei i ee Primeneniya, 2006, Volume 51, Issue 2, Pages 382–385
DOI: https://doi.org/10.4213/tvp60
(Mi tvp60)
 

This article is cited in 3 scientific papers (total 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
Full-text PDF (502 kB) Citations (3)
References:
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
English version:
Theory of Probability and its Applications, 2007, Volume 51, Issue 2, Pages 359–362
DOI: https://doi.org/10.1137/S0040585X97982426
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. M. Kruglov, “Growth of sums of pairwise independent random variables with infinite means”, Teor. Veroyatnost. i Primenen., 51:2 (2006), 382–385; Theory Probab. Appl., 51:2 (2007), 359–362
Citation in format AMSBIB
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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