IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v32y1997i2p167-174.html
   My bibliography  Save this article

A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces

Author

Listed:
  • Adler, André
  • Rosalsky, Andrew
  • Volodin, Andrej I.

Abstract

For weighted sums of the form Sn = [summation operator]j=1kn anj(Vnj - cnj) where {anj, 1[less-than-or-equals, slant]j[less-than-or-equals, slant]kn

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:2:p:167-174
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(97)85593-9
    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

    as
    1. Gut, Allan, 1992. "The weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 14(1), pages 49-52, May.
    2. Dug Hun Hong & Kwang Sik Oh, 1995. "On the weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 22(1), pages 55-57, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. 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.
    2. 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.
    3. Quang, Nguyen Van & Huan, Nguyen Van, 2009. "On the strong law of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1891-1899, September.

    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. 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.
    2. 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.
    3. Sung, Soo Hak, 1998. "Weak law of large numbers for arrays," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 101-105, June.
    4. 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.
    5. 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.
    6. Ankirchner, Stefan & Kruse, Thomas & Urusov, Mikhail, 2017. "WLLN for arrays of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 73-78.
    7. 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.
    8. 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.
    9. Meng, Yanjiao & Lin, Zhengyan, 2009. "On the weak laws of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2405-2414, December.
    10. 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.
    11. 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.
    12. 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.

    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:32:y:1997:i:2:p:167-174. 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.