Acta Mathematica Sinica, English Series

, Volume 23, Issue 4, pp 613–622 | Cite as

Dimensional Properties of Fractional Brownian Motion

  • Dong Sheng WuEmail author
  • Yi Min Xiao*Email author


Let B α = {B α (t), t ∈ ℝ N } be an (N, d)-fractional Brownian motion with Hurst index α ∈ (0, 1). By applying the strong local nondeterminism of B α , we prove certain forms of uniform Hausdorff dimension results for the images of B α 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 


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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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