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On intersections of independent space–time anisotropic Gaussian fields

Author

Listed:
  • Chen, Zhenlong
  • Wang, Jun
  • Wu, Dongsheng

Abstract

Let XH={XH(s),s∈RN1} and XK={XK(t),t∈RN2} be two independent centered space–time anisotropic Gaussian random fields taking values in Rd. In this paper, we study the existence of intersections of XH and XK. Furthermore, we determine the Hausdorff dimensions of the set of intersection times and the set of intersection points of the random fields, respectively. Our results generalize the corresponding results of Chen and Xiao (2012).

Suggested Citation

  • Chen, Zhenlong & Wang, Jun & Wu, Dongsheng, 2020. "On intersections of independent space–time anisotropic Gaussian fields," Statistics & Probability Letters, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:stapro:v:166:y:2020:i:c:s0167715220301772
    DOI: 10.1016/j.spl.2020.108874
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    References listed on IDEAS

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    1. Rosen, Jay, 1987. "The intersection local time of fractional Brownian motion in the plane," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 37-46, October.
    2. Li, Yuqiang & Xiao, Yimin, 2011. "Multivariate operator-self-similar random fields," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1178-1200, June.
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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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