IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v16y2003i3d10.1023_a1025684513749.html
   My bibliography  Save this article

The Law of the Logarithm for Weighted Sums of Independent Random Variables

Author

Listed:
  • D. Li

    (Lakehead University)

  • R. J. Tomkins

    (University of Regina, Regina)

Abstract

Let X,X n ;n≥1 be a sequence of real-valued i.i.d. random variables with E(X)=0. Assume B(u) is positive, strictly increasing and regularly-varying at infinity with index 1/2≤α x) = o(\log x){\text{ }}as{\text{ x}} \to \infty $$ and $$\mathop {\lim }\limits_{x \to \infty } \sup \frac{{n\log nE(X^2 I_{\left\{ {X^2

Suggested Citation

  • D. Li & R. J. Tomkins, 2003. "The Law of the Logarithm for Weighted Sums of Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 16(3), pages 519-542, July.
    • Handle: RePEc:spr:jotpro:v:16:y:2003:i:3:d:10.1023_a:1025684513749
    DOI: 10.1023/A:1025684513749
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1025684513749
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1025684513749?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Li, D. L. & Rao, M. B. & Wang, X. C., 1995. "On the Strong Law of Large Numbers and the Law of the Logarithm for Weighted Sums of Independent Random Variables with Multidimensional Indices," Journal of Multivariate Analysis, Elsevier, vol. 52(2), pages 181-198, February.
    2. Li, Deli, 1996. "Bounded and compact laws of the logarithm for B-valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 189-209, November.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Pingyan & Chen, Ran, 2010. "A remark on LSL for weighted sums of i.i.d random elements," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1329-1334, September.
    2. Sung, Soo Hak, 2009. "A law of the single logarithm for weighted sums of i.i.d. random elements," Statistics & Probability Letters, Elsevier, vol. 79(10), pages 1351-1357, May.
    3. Li, Deli & Bhaskara Rao, M. & Tomkins, R. J., 2001. "The Law of the Iterated Logarithm and Central Limit Theorem for L-Statistics," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 191-217, August.
    4. Li, Deli, 1996. "Bounded and compact laws of the logarithm for B-valued random variables," Stochastic Processes and their Applications, Elsevier, vol. 63(2), pages 189-209, November.
    5. Feng, Xinwei, 2019. "Law of the logarithm for weighted sums of negatively dependent random variables under sublinear expectation," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 132-141.
    6. Chen, Pingyan & Hao, Chunyan, 2011. "A remark on the law of the logarithm for weighted sums of random variables with multidimensional indices," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1808-1812.

    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:spr:jotpro:v:16:y:2003:i:3:d:10.1023_a:1025684513749. 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.

    If CitEc recognized a bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.