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
*Research partially supported by NSF Grant DMS-0404729