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Hausdorff Measure of the Range of Space–Time Anisotropic Gaussian Random Fields

Author

Listed:
  • Wenqing Ni

    (Zhejiang Gongshang University
    Jimei University)

  • Zhenlong Chen

    (Zhejiang Gongshang University)

Abstract

Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ X = { X ( t ) ∈ R d , t ∈ R N } be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed. Under certain mild conditions, we determine the exact Hausdorff measure function for the range $$X([0,1]^N)$$ X ( [ 0 , 1 ] N ) . Our result extends those in Talagrand (Ann Probab 23:767–775, 1995) for fractional Brownian motion and Luan and Xiao (J Fourier Anal Appl 18:118–145, 2012) for time-anisotropic and space-isotropic Gaussian random fields.

Suggested Citation

  • Wenqing Ni & Zhenlong Chen, 2021. "Hausdorff Measure of the Range of Space–Time Anisotropic Gaussian Random Fields," Journal of Theoretical Probability, Springer, vol. 34(1), pages 264-282, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00964-3
    DOI: 10.1007/s10959-019-00964-3
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    References listed on IDEAS

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    1. Ni, Wenqing & Chen, Zhenlong, 2016. "Hitting probabilities of a class of Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 145-155.
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    Cited by:

    1. Weijie Yuan & Zhenlong Chen, 2024. "Hausdorff Measure and Uniform Dimension for Space-Time Anisotropic Gaussian Random Fields," Journal of Theoretical Probability, Springer, vol. 37(3), pages 2304-2329, September.

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