A uniform result for the dimension of fractional Brownian motion level sets

Lara Daw

Statistics & Probability Letters, 2021, vol. 169, issue C

Abstract: Let B={Bt:t≥0} be a real-valued fractional Brownian motion of index H∈(0,1). We prove that the macroscopic Hausdorff dimension of the level sets Lx=t∈R+:Bt=x is, with probability one, equal to 1−H for all x∈R.

Keywords: Level sets; Fractional Brownian motion; Local times; Macroscopic Hausdorff dimension (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1016/j.spl.2020.108984

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