Skip to main content
SpringerLink
Log in

Asymptotic Properties and Hausdorff Dimensions of Fractional Brownian Sheets

  • Published:
Journal of Fourier Analysis and Applications Aims and scope Submit manuscript

Abstract

Let BH = {BH(t ), t ∈ ℝN} be an (N, d)-fractional Brownian sheet with index H = (H1, . . . , HN) ∈ (0, 1)N. The uniform and local asymptotic properties of BH are proved by using wavelet methods. The Hausdorff and packing dimensions of the range BH ([0, 1]N), the graph Gr BH ([0, 1]N) and the level set are determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. U.M.R CNRS 8524, Laboratoire Paul Painleve, Bat.M2, Universite Lille 1, 59 655 Villeneuve d’Ascq Cedex and U.M.R CNRS 8020 CLAREE, IAE de Lille 104, Avenue du Peuple Belge, 59043 Lille Cedex, France

    Antoine Ayache

  2. Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, MI 48823, USA

    Yimin Xiao

Authors
  1. Antoine Ayache
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yimin Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Antoine Ayache or Yimin Xiao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ayache, A., Xiao, Y. Asymptotic Properties and Hausdorff Dimensions of Fractional Brownian Sheets. J Fourier Anal Appl 11, 407–439 (2005). https://doi.org/10.1007/s00041-005-4048-3

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00041-005-4048-3

Keywords

Search

Navigation