IDEAS home Printed from
   My bibliography  Save this article

An intermediate Baum-Katz theorem


  • Gut, Allan
  • Stadtmüller, Ulrich


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

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    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.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:81:y:2011:i:10:p:1486-1492. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.