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The Csörgő–Révész moduli of non-differentiability of fractional Brownian motion

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  • Wang, Wensheng
  • Xiao, Yimin

Abstract

We establish the exact moduli of non-differentiability of fractional Brownian motion. As an application of the result, we prove that the uniform Hölder condition for the maximum local times of fractional Brownian motion obtained in Xiao (1997) is optimal.

Suggested Citation

  • Wang, Wensheng & Xiao, Yimin, 2019. "The Csörgő–Révész moduli of non-differentiability of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 150(C), pages 81-87.
    • Handle: RePEc:eee:stapro:v:150:y:2019:i:c:p:81-87
    DOI: 10.1016/j.spl.2019.02.016
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    References listed on IDEAS

    as
    1. Ortega, Joaquín, 1984. "On the size of the increments of nonstationary Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 18(1), pages 47-56, September.
    2. Shao, Qi-Man, 2003. "A Gaussian correlation inequality and its applications to the existence of small ball constant," Stochastic Processes and their Applications, Elsevier, vol. 107(2), pages 269-287, October.
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