Packing dimension of the image of fractional Brownian motion

https://doi.org/10.1016/S0167-7152(96)00151-4Get rights and content

Abstract

Let X(t) (t ∈ RN) be a fractional Brownian motion of index α in Rd. For any analytic set E ⊆ RN, we show that DimX(E)=1αDimαdE a.s., where DimE is the packing dimension of E and DimsE is the packing dimension profile of E defined by Falconer and Howroyd (1995).

References (12)

  • K.J. Falconer

    Fractal Geometry — Mathematical Foundations And Applications

    (1990)
  • K.J. Falconer et al.

    Packing dimensions for projections and dimension profiles

  • X. Hu et al.

    Fractal properties of products and projections of measures in Rd

  • J.-P. Kahane

    Some Random Series of Functions

    (1985)
  • Lin Hounan et al.

    Dimension properties of the sample paths of self-similar processes

    Acta Math. Sinica

    (1994)
  • P. Mattila

    Geometry of Sets and Measures in Euclidean Spaces

    (1995)
There are more references available in the full text version of this article.

Cited by (41)

  • Fractal dimensions of the Rosenblatt process

    2023, Stochastic Processes and their Applications
  • Packing dimensions of the images of Gaussian random fields

    2015, Statistics and Probability Letters
View all citing articles on Scopus
View full text