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Fractal dimensions of rough differential equations driven by fractional Brownian motions

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  • Lou, Shuwen
  • Ouyang, Cheng

Abstract

In this work we study fractal properties of a d-dimensional rough differential equation driven by fractional Brownian motions with Hurst parameter H>14. In particular, we show that the Hausdorff dimension of the sample paths of the solution is min{d,1H} and that the Hausdorff dimension of the level set Lx={t∈[ϵ,1]:Xt=x} is 1−dH with positive probability when dH<1.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:8:p:2410-2429
    DOI: 10.1016/j.spa.2016.02.005
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    References listed on IDEAS

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    1. Xiao, Yimin, 1997. "Packing dimension of the image of fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 379-387, May.
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    Cited by:

    1. Ouyang, Cheng & Shi, Yinghui & Wu, Dongsheng, 2018. "Mutual intersection for rough differential systems driven by fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 83-91.
    2. Lou, Shuwen & Ouyang, Cheng, 2017. "Local times of stochastic differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3643-3660.

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