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

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).

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Year of publication:	2014
Authors:	Chen, Pingyan ; Sung, Soo Hak
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 94.2014, C, p. 63-68
Publisher:	Elsevier
Subject:	Baum–Katz law \| Sums of i.i.d. random variables \| Convergence rates

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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