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

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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)<∞, where 1<p<2.

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Acknowledgements

The author would like to thank the referee for helpful comments. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0013131).

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  1. Department of Applied Mathematics, Pai Chai University, Taejon, 302-735, South Korea

    Soo Hak Sung

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  1. Soo Hak Sung
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Sung, S.H. Marcinkiewicz–Zygmund Type Strong Law of Large Numbers for Pairwise i.i.d. Random Variables. J Theor Probab 27, 96–106 (2014). https://doi.org/10.1007/s10959-012-0417-4

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  • DOI: https://doi.org/10.1007/s10959-012-0417-4

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