IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v49y2000i2p113-118.html
   My bibliography  Save this article

A note on logarithmic tail asymptotics and mixing

Author

Listed:
  • Gantert, Nina

Abstract

Let Y1,Y2,... be a stationary, ergodic sequence of non-negative random variables with heavy tails. Under mixing conditions, we derive logarithmic tail asymptotics for the distributions of the arithmetic mean. If not all moments of Y1 are finite, these logarithmic asymptotics amount to a weaker form of the Baum-Katz law. Roughly, the sum of i.i.d. heavy-tailed non-negative random variables has the same behaviour as the largest term in the sum, and this phenomenon persists for weakly dependent random variables. Under mixing conditions, the rate of convergence in the law of large numbers is, as in the i.i.d. case, determined by the tail of the distribution of Y1. There are many results which make these statements more precise. The paper describes a particularly simple way to carry over logarithmic tail asymptotics from the i.i.d. to the mixing case.

Suggested Citation

  • Gantert, Nina, 2000. "A note on logarithmic tail asymptotics and mixing," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 113-118, August.
    • Handle: RePEc:eee:stapro:v:49:y:2000:i:2:p:113-118
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(00)00037-7
    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.

    Citations

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


    Cited by:

    1. Li, Deli & Miao, Yu & Stoica, George, 2022. "A general large deviation result for partial sums of i.i.d. super-heavy tailed random variables," Statistics & Probability Letters, Elsevier, vol. 184(C).
    2. Harri Nyrhinen, 2009. "On Large Deviations of Multivariate Heavy-Tailed Random Walks," Journal of Theoretical Probability, Springer, vol. 22(1), pages 1-17, March.
    3. Miao, Yu & Li, Deli, 2024. "A general logarithmic asymptotic behavior for partial sums of i.i.d. random variables," Statistics & Probability Letters, Elsevier, vol. 208(C).

    Corrections

    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:49:y:2000:i:2:p:113-118. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.