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On the strong law of large numbers for pairwise i.i.d. random variables with general moment conditions

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  • Sung, Soo Hak

Abstract

Let {an,n≥1} be a sequence of positive constants with an/n↑ and let {X,Xn,n≥1} be a sequence of pairwise independent identically distributed random variables. In this paper, we obtain the strong law of large numbers and complete convergence for the sequence {X,Xn,n≥1}, which are equivalent to the general moment condition ∑n=1∞P(|X|>an)<∞. We obtain, as a corollary, the strong law of large numbers due to Kruglov [Kruglov, V.M., 2008. A strong law of large numbers for pairwise independent identically distributed random variables with infinite means. Statist. Probab. Lett. 78, 890–895].

Suggested Citation

  • Sung, Soo Hak, 2013. "On the strong law of large numbers for pairwise i.i.d. random variables with general moment conditions," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 1963-1968.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:9:p:1963-1968
    DOI: 10.1016/j.spl.2013.05.009
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    References listed on IDEAS

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    1. Kruglov, Victor M., 2008. "A strong law of large numbers for pairwise independent identically distributed random variables with infinite means," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 890-895, May.
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