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

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  • Daw, Lara

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.

Suggested Citation

  • Daw, Lara, 2021. "A uniform result for the dimension of fractional Brownian motion level sets," Statistics & Probability Letters, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:stapro:v:169:y:2021:i:c:s016771522030287x
    DOI: 10.1016/j.spl.2020.108984
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    References listed on IDEAS

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    1. Baudoin, Fabrice & Nualart, David, 2003. "Equivalence of Volterra processes," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 327-350, October.
    2. Seuret, Stéphane & Yang, Xiaochuan, 2019. "On sojourn of Brownian motion inside moving boundaries," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 978-994.
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    Cited by:

    1. Daw, Lara & Kerchev, George, 2023. "Fractal dimensions of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 544-571.

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