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

Soo Hak Sung ()
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Soo Hak Sung: Pai Chai University

Journal of Theoretical Probability, 2014, vol. 27, issue 1, 96-106

Abstract: 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)

Keywords: Strong law of large numbers; Almost sure convergence; Pairwise independent random variables; 60F15 (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10959-012-0417-4

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