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Packing dimension of the image of fractional Brownian motion

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  • Xiao, Yimin

Abstract

Let be a fractional Brownian motion of index [alpha] in d. For any analytic set , we show that , where DimE is the packing dimension of E and DimsE is the packing dimension profile of E defined by Falconer and Howroyd (1995).

Suggested Citation

  • Xiao, Yimin, 1997. "Packing dimension of the image of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 379-387, May.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:4:p:379-387
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    Citations

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    Cited by:

    1. Meerschaert, Mark M. & Xiao, Yimin, 2005. "Dimension results for sample paths of operator stable Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 55-75, January.
    2. Li, Jinjun, 2011. "A class of probability distribution functions preserving the packing dimension," Statistics & Probability Letters, Elsevier, vol. 81(12), pages 1782-1791.
    3. Daw, Lara & Kerchev, George, 2023. "Fractal dimensions of the Rosenblatt process," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 544-571.
    4. Lou, Shuwen & Ouyang, Cheng, 2016. "Fractal dimensions of rough differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2410-2429.
    5. Falconer, Kenneth J., 2022. "Intermediate dimension of images of sequences under fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 182(C).
    6. Du, Yali & Miao, Junjie & Wu, Dongsheng & Xiao, Yimin, 2015. "Packing dimensions of the images of Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 209-217.
    7. Xiao, Yimin, 2009. "A packing dimension theorem for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 79(1), pages 88-97, January.
    8. Stuart A. Burrell, 2022. "Dimensions of Fractional Brownian Images," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2217-2238, December.

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