Journal of Fourier Analysis and Applications

, Volume 11, Issue 4, pp 407–439

Asymptotic Properties and Hausdorff Dimensions of Fractional Brownian Sheets

Article

DOI: 10.1007/s00041-005-4048-3

Cite this article as:
Ayache, A. & Xiao, Y. J Fourier Anal Appl (2005) 11: 407. doi:10.1007/s00041-005-4048-3

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.

Copyright information

© Birkhauser Boston 2005

Authors and Affiliations

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