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Local Nondeterminism and Hausdorff Dimension

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

Abstract

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.

Keywords

Gaussian Process Hausdorff Dimension Fractional Brownian Motion Sample Function Gaussian Random Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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