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

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  • Chen, Pingyan
  • Sung, Soo Hak

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).

Suggested Citation

  • Chen, Pingyan & Sung, Soo Hak, 2014. "A Baum–Katz theorem for i.i.d. random variables with higher order moments," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 63-68.
    • Handle: RePEc:eee:stapro:v:94:y:2014:i:c:p:63-68
    DOI: 10.1016/j.spl.2014.07.005
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    References listed on IDEAS

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    1. Gut, Allan & Stadtmüller, Ulrich, 2011. "An intermediate Baum-Katz theorem," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1486-1492, October.
    2. Lanzinger, Hartmut, 1998. "A Baum-Katz theorem for random variables under exponential moment conditions," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 89-95, August.
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    2. Gut, Allan & Stadtmüller, Ulrich, 2011. "An intermediate Baum-Katz theorem," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1486-1492, October.

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