IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v63y1996i2p189-209.html
   My bibliography  Save this article

Bounded and compact laws of the logarithm for B-valued random variables

Author

Listed:
  • Li, Deli

Abstract

In this paper, we study a version of the law of the logarithm in a Banach space setting. Some necessary and some sufficient conditions are presented for the law of the logarithm for B-valued random variables. The law of the logarithm, the law of the iterated logarithm and the central limit theorem are shown to be equivalent for finite-dimentional B-valued random variables. However, this statement is not true for infinite-dimensional case. Under the central limit theorem, the law of the logarithm is shown to be equivalent to some certain moment condition. The law of the iterated logarithm implies the law of the logarithm, but the converse is not true. All methods used in this paper are quite standard in probability in Banach spaces except for some modifications. We made an effort to solve this problem completely in a Banach space using both the isoperimetric methods and the Gaussian randomization technique, but we were not successful.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:63:y:1996:i:2:p:189-209
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0304-4149(96)00067-1
    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. 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.
    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. 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. 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.
    3. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    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.

    More about this item

    Keywords

    60B12 60F15 G0G50;

    JEL classification:

    Statistics

    Access and download statistics

    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:spapps:v:63:y:1996:i:2:p:189-209. 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/505572/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.