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Path Properties of a Generalized Fractional Brownian Motion

Author

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  • Tomoyuki Ichiba

    (University of California, Santa Barbara)

  • Guodong Pang

    (Pennsylvania State University)

  • Murad S. Taqqu

    (Boston University)

Abstract

The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power-law shape function and non-stationary noises with a power-law variance function. In this paper, we study sample path properties of the generalized fractional Brownian motion, including Hölder continuity, path differentiability/non-differentiability, and functional and local law of the iterated logarithms.

Suggested Citation

  • Tomoyuki Ichiba & Guodong Pang & Murad S. Taqqu, 2022. "Path Properties of a Generalized Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 35(1), pages 550-574, March.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:1:d:10.1007_s10959-020-01066-1
    DOI: 10.1007/s10959-020-01066-1
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    References listed on IDEAS

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