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An intermediate Baum-Katz theorem

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  • Gut, Allan
  • Stadtmüller, Ulrich

Abstract

We extend the classical Hsu-Robbins-Erdos theorem to the case when all moments exist, but the moment generating function does not, viz., we assume that Eexp{(log+X)[alpha]} 1. We also present multi-index versions of the same and of a related result due to Lanzinger in which the assumption is that Eexp{X[alpha]}

Suggested Citation

  • Gut, Allan & Stadtmüller, Ulrich, 2011. "An intermediate Baum-Katz theorem," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1486-1492, October.
  • Handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1486-1492
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    References listed on IDEAS

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    1. Chen, Robert, 1978. "A remark on the tail probability of a distribution," Journal of Multivariate Analysis, Elsevier, vol. 8(2), pages 328-333, June.
    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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    Cited by:

    1. Qiu, Dehua & Chen, Pingyan, 2014. "Complete moment convergence for i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 76-82.
    2. 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.

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