Chen, Pingyan; Sung, Soo Hak - In: Statistics & Probability Letters 94 (2014) C, pp. 63-68
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).
