Local Nondeterminism and Hausdorff Dimension

  • Ditlev Monrad
  • Loren D. Pitt
Part of the Progress in Probability and Statistics book series (PRPR, volume 13)


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
$$E[{{e}^{i<u,X(t)-X(s)>}}]={{e}^{-\frac{1}{2}|u{{|}^{2}}|t-s{{|}^{\alpha }}}}$$
for all u ∈ ℝd and s, t ∈ ℝN. If α = 1, then we have Lévy’s multiparameter Brownian motion.


Gaussian Process Hausdorff Dimension Fractional Brownian Motion Sample Function Gaussian Random Field 
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Copyright information

© Birkhäuser Boston 1987

Authors and Affiliations

  • Ditlev Monrad
    • 1
    • 2
  • Loren D. Pitt
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA
  2. 2.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA

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