IDEAS home Printed from
   My bibliography  Save this article

On the pointwise central limit theorem and mixtures of stable distributions


  • Berkes, I.
  • Csáki, E.


Let X1, X2, ... be i.i.d. r.v.'s with EX1 = 0. EX21 - 1 and put Sn = X1 + ... + Xn. We investigate the a.s. limiting behavior of for general norming sequences (ak). The pointwise central limit theorem shows that LN converges a.s. to the normal distribution if ak = [radical sign]k; in our paper we prove the surprising result that for suitably chosen (ak) the expression LN can converge also to non-Gaussian limits, in particular, any symmetric stable distribution is a possible limit of LN. We shall determine the class of limit distributions of LN and extend the result to the case when Xn belong to the domain of attraction of a stable law.

Suggested Citation

  • Berkes, I. & Csáki, E., 1996. "On the pointwise central limit theorem and mixtures of stable distributions," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 361-368, September.
  • Handle: RePEc:eee:stapro:v:29:y:1996:i:4:p:361-368

    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.


    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:29:y:1996:i:4:p:361-368. 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.

    We have no references for this item. You can help adding them by using 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.