A Baum–Katz theorem for i.i.d. random variables with higher order moments

Pingyan Chen and Soo Hak Sung

Statistics & Probability Letters, 2014, vol. 94, issue C, 63-68

Abstract: For a sequence of i.i.d. random variables {X,Xn,n≥1} with EX=0 and Eexp{(log|X|)α}<∞ for some α>1, Gut and Stadtmüller (2011) proved a Baum–Katz theorem. In this paper, it is proved that Eexp{(log|X|)α}<∞ if and only if ∑n=1∞exp{(logn)α}n−2(logn)α−1P(|Sn|>n)<∞, where Sn=∑i=1nXi. This result improves the corresponding one of Gut and Stadtmüller (2011).

Keywords: Baum–Katz law; Sums of i.i.d. random variables; Convergence rates (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2014.07.005

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