, Volume 23, Issue 4, pp 613-622
Date: 15 Feb 2007

Dimensional Properties of Fractional Brownian Motion

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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.

*Research partially supported by NSF Grant DMS-0404729