Local nondeterminism and Hausdorff dimension

Let X = {X(t,ω): t ∈ ℝN} denote d-dimensional fractional Brownian motion of index α ∈ (0,2), normalized such that X(0) = 0 and $$E[{{e}^{i }}]={{e}^{-\frac{1}{2}|u{{|}^{2}}|t-s{{|}^{\alpha }}}}$$ for all u ∈ ℝd and s, t ∈ ℝN. If α = 1, then we have Levy’s multiparameter Brownian motion.

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