IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v122y2017icp63-72.html
   My bibliography  Save this article

Strong laws for sequences in the vicinity of the LIL

Author

Listed:
  • Gut, Allan
  • Stadtmüller, Ulrich

Abstract

The present paper is devoted to strong laws of large numbers under moment conditions near those of the law of the iterated logarithm (LIL) for i.i.d sequences. More precisely, we wish to investigate possible limit theorems under moment conditions which are stronger than p for any p<2, in which case we know that there is a.s. convergence to 0, and weaker than EX2<∞, in which case the LIL holds.

Suggested Citation

  • Gut, Allan & Stadtmüller, Ulrich, 2017. "Strong laws for sequences in the vicinity of the LIL," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 63-72.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:63-72
    DOI: 10.1016/j.spl.2016.10.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715216302267
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2016.10.027?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. Gut, Allan, 1992. "The weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 49-52, May.
    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. Clément de Chaisemartin & Luc Behaghel, 2020. "Estimating the Effect of Treatments Allocated by Randomized Waiting Lists," Econometrica, Econometric Society, vol. 88(4), pages 1453-1477, July.
    2. Adler, André & Rosalsky, Andrew & Volodin, Andrej I., 1997. "A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 32(2), pages 167-174, March.
    3. Hong, Dug Hun & Cabrera, Manuel Ordóñez & Sung, Soo Hak & Volodin, Andrei I., 2000. "On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces," Statistics & Probability Letters, Elsevier, vol. 46(2), pages 177-185, January.
    4. Hu, Tien-Chung & Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 155-164, January.
    5. Sung, Soo Hak, 1998. "Weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 101-105, June.
    6. Hong, Dug Hun, 1996. "On the weak law of large numbers for randomly indexed partial sums for arrays," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 127-130, June.
    7. Christofides, Tasos C. & Serfling, Robert, 1998. "U-statistics on a lattice of I.I.D. random variables," Statistics & Probability Letters, Elsevier, vol. 40(3), pages 293-303, October.
    8. Cabrera, Manuel Ordóñez & Volodin, Andrei I., 2001. "On conditional compactly uniform pth-order integrability of random elements in Banach spaces," Statistics & Probability Letters, Elsevier, vol. 55(3), pages 301-309, December.
    9. Sung, Soo Hak, 1999. "Weak law of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 293-298, April.
    10. Sung, Soo Hak & Hu, Tien-Chung & Volodin, Andrei, 2005. "On the weak laws for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 291-298, May.
    11. Ankirchner, Stefan & Kruse, Thomas & Urusov, Mikhail, 2017. "WLLN for arrays of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 73-78.

    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:122:y:2017:i:c:p:63-72. 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: 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.