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Teor. Veroyatnost. i Primenen., 2006, Volume 51, Issue 2, Pages 382–385 (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

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 $S_n=X_1+…+X_n$ 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.

DOI: https://doi.org/10.4213/tvp60

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

Bibliographic databases:

Received: 21.06.2004

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kruglov V.M., “A strong law of large numbers for pairwise independent identically distributed random variables with infinite means”, Statist. Probab. Lett., 78:7 (2008), 890–895  crossref  mathscinet  zmath  isi  elib  scopus
    2. Sung Soo Hak, Lisawadi S., Volodin A., “Weak laws of large numbers for arrays under a condition of uniform integrability”, J. Korean Math. Soc., 45:1 (2008), 289–300  crossref  mathscinet  zmath  isi  scopus
    3. Van Thanh Le, Ngoc Anh Vu, “A strong limit theorem for sequences of blockwise and pairwise $m$-dependent random variables”, Bull. Korean Math. Soc., 48:2 (2011), 343–351  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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