Intermediate dimension of images of sequences under fractional Brownian motion

Kenneth John Falconer*

*Corresponding author for this work

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Abstract

We show that the almost sure θ-intermediate dimension of the image of the set Fp ={0, 1,1/2p,1/3p,...} under index-h fractional Brownian motion is θ/(ph+θ), a value that is smaller than that given by directly applying the Hölder bound for fractional Brownian motion. In particular this establishes the box-counting dimension of these images.
Original languageEnglish
Article number109300
Number of pages6
JournalStatistics and Probability Letters
Volume182
Early online date5 Nov 2021
DOIs
Publication statusPublished - Mar 2022

Keywords

  • Fractional Brownian motion
  • Fractal
  • Intermediate dimension
  • Hausdorff dimension
  • Box-counting dimension

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