ORIGINAL ARTICLES

Acta Mathematica Sinica, English Series

, Volume 23, Issue 4, pp 613-622

First online:

Dimensional Properties of Fractional Brownian Motion

  • Dong Sheng WuAffiliated withDepartment of Statistics and Probability, A-413 Wells Hall, Michigan State University Email author 
  • , Yi Min Xiao*Affiliated withDepartment of Statistics and Probability, A-413 Wells Hall, Michigan State University Email author 

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Abstract

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.

Keywords

fractional Brownian motion Hausdorff dimension uniform dimension results strong local nondeterminism

MR (2000) Subject Classification

60G15 60G17