Intermediate dimension of images of sequences under fractional Brownian motion

Kenneth J. Falconer

Statistics & Probability Letters, 2022, vol. 182, issue C

Abstract: We show that the almost sure θ-intermediate dimension of the image of the set Fp={0,1,12p,13p,…} under index-h fractional Brownian motion is θph+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.

Keywords: Fractional Brownian motion; Fractal; Intermediate dimension; Hausdorff dimension; Box-counting dimension (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spl.2021.109300

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