Acta Mathematica Sinica, English Series

, Volume 23, Issue 4, pp 613–622

Dimensional Properties of Fractional Brownian Motion


DOI: 10.1007/s10114-005-0928-3

Cite this article as:
Wu, D.S. & Xiao*, Y.M. Acta Math Sinica (2007) 23: 613. doi:10.1007/s10114-005-0928-3


Let Bα = {Bα(t), t ∈ ℝN} be an (N, d)-fractional Brownian motion with Hurst index α ∈ (0, 1). By applying the strong local nondeterminism of Bα, we prove certain forms of uniform Hausdorff dimension results for the images of Bα when N >αd. Our results extend those of Kaufman for one-dimensional Brownian motion.


fractional Brownian motion Hausdorff dimension uniform dimension results strong local nondeterminism 

MR (2000) Subject Classification

60G15 60G17 

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Department of Statistics and Probability, A-413 Wells HallMichigan State UniversityEast LansingUSA

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