Abstract
Let B α = {B α(t), t ∈ ℝN} 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.
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*Research partially supported by NSF Grant DMS-0404729
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Wu, D.S., Xiao*, Y.M. Dimensional Properties of Fractional Brownian Motion. Acta Math Sinica 23, 613–622 (2007). https://doi.org/10.1007/s10114-005-0928-3
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DOI: https://doi.org/10.1007/s10114-005-0928-3