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Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces

Author

Listed:
  • Tianshi Lu

    (Wichita State University)

  • Chunsheng Ma

    (Wichita State University)

Abstract

The covariance matrix function is characterized in this paper for a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the compact two-point homogeneous space. Necessary and sufficient conditions are derived for a symmetric and continuous matrix function to be an isotropic covariance matrix function on all compact two-point homogeneous spaces. It is also shown that, for a symmetric and continuous matrix function with compact support, if it makes an isotropic covariance matrix function in the Euclidean space, then it makes an isotropic covariance matrix function on the sphere or the real projective space.

Suggested Citation

  • Tianshi Lu & Chunsheng Ma, 2020. "Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1630-1656, September.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:3:d:10.1007_s10959-019-00920-1
    DOI: 10.1007/s10959-019-00920-1
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    References listed on IDEAS

    as
    1. Chunsheng Ma, 2017. "Time Varying Isotropic Vector Random Fields on Spheres," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1763-1785, December.
    2. Cheng, Dan, 2016. "Excursion probability of certain non-centered smooth Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 883-905.
    3. Douglas Azevedo & Victor S. Barbosa, 2017. "Covering numbers of isotropic reproducing kernels on compact two-point homogeneous spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 290(16), pages 2444-2458, November.
    4. Renxiang Wang & Juan Du & Chunsheng Ma, 2014. "Covariance Matrix Functions of Isotropic Vector Random Fields," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 2081-2093, May.
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    Cited by:

    1. Lu, Tianshi & Du, Juan & Ma, Chunsheng, 2022. "Stochastic comparison for elliptically contoured random fields," Statistics & Probability Letters, Elsevier, vol. 189(C).
    2. Chunsheng Ma, 2023. "Vector Random Fields on the Probability Simplex with Metric-Dependent Covariance Matrix Functions," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1922-1938, September.

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