IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v106y2015icp228-238.html
   My bibliography  Save this article

The Fourier dimension of Brownian limsup fractals

Author

Listed:
  • Potgieter, Paul

Abstract

Robert Kaufman’s proof that the set of rapid points of Brownian motion has a Fourier dimension equal to its Hausdorff dimension was first published in 1974. Some of the original arguments presented by Kaufman are not clear, hence this paper presents a new version of the construction and incorporates some recent results in order to establish a slightly weaker version of Kaufman’s theorem. This weaker version still implies that the Fourier and Hausdorff dimensions of Brownian rapid points are equal. The method of proof can then be extended to show that functionally determined rapid points of Brownian motion also form Salem sets for absolutely continuous functions of finite energy.

Suggested Citation

  • Potgieter, Paul, 2015. "The Fourier dimension of Brownian limsup fractals," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 228-238.
    • Handle: RePEc:eee:stapro:v:106:y:2015:i:c:p:228-238
    DOI: 10.1016/j.spl.2015.07.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215002710
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.07.030?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. Fouché, Willem L. & Mukeru, Safari, 2013. "On the Fourier structure of the zero set of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 459-466.
    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.

      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:106:y:2015:i:c:p:228-238. 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.