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Intermediate dimension of images of sequences under fractional Brownian motion

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  • Falconer, Kenneth J.

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.

Suggested Citation

  • Falconer, Kenneth J., 2022. "Intermediate dimension of images of sequences under fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:stapro:v:182:y:2022:i:c:s0167715221002625
    DOI: 10.1016/j.spl.2021.109300
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    References listed on IDEAS

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    1. Xiao, Yimin, 1997. "Packing dimension of the image of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 379-387, May.
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