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Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables

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  • Soo Hak Sung

    (Pai Chai University)

Abstract

Etemadi (in Z. Wahrscheinlichkeitstheor. Verw. Geb. 55, 119–122, 1981) proved that the Kolmogorov strong law of large numbers holds for pairwise independent identically distributed (pairwise i.i.d.) random variables. However, it is not known yet whether the Marcinkiewicz–Zygmund strong law of large numbers holds for pairwise i.i.d. random variables. In this paper, we obtain the Marcinkiewicz–Zygmund type strong law of large numbers for pairwise i.i.d. random variables {X n ,n≥1} under the moment condition E|X 1| p (loglog|X 1|)2(p−1)

Suggested Citation

  • Soo Hak Sung, 2014. "Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables," Journal of Theoretical Probability, Springer, vol. 27(1), pages 96-106, March.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:1:d:10.1007_s10959-012-0417-4
    DOI: 10.1007/s10959-012-0417-4
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    References listed on IDEAS

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    1. Martikainen, Alexander, 1995. "On the strong law of large numbers for sums of pairwise independent random variables," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 21-26, October.
    2. Etemadi, N., 1983. "Stability of sums of weighted nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 361-365, June.
    3. Etemadi, Nasrollah, 1983. "On the laws of large numbers for nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 187-193, March.
    4. 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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    Cited by:

    1. Vu T. N. Anh & Nguyen T. T. Hien & Le V. Thanh & Vo T. H. Van, 2021. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences," Journal of Theoretical Probability, Springer, vol. 34(1), pages 331-348, March.
    2. Shuxia Guo & Zhe Meng, 2023. "The Marcinkiewicz–Zygmund-Type Strong Law of Large Numbers with General Normalizing Sequences under Sublinear Expectation," Mathematics, MDPI, vol. 11(23), pages 1-21, November.

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