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Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

Author

Listed:
  • Chunsheng Ma

    (Wichita State University)

  • Anatoliy Malyarenko

    (Mälardalen University)

Abstract

A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field which involves Jacobi polynomials and the distance defined on the compact two-point homogeneous space.

Suggested Citation

  • Chunsheng Ma & Anatoliy Malyarenko, 2020. "Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces," Journal of Theoretical Probability, Springer, vol. 33(1), pages 319-339, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-018-0872-7
    DOI: 10.1007/s10959-018-0872-7
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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. 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.
    3. Ma, Chunsheng, 2013. "K-distributed vector random fields in space and time," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1143-1150.
    4. 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.
    5. Baldi, Paolo & Rossi, Maurizia, 2014. "Representation of Gaussian isotropic spin random fields," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1910-1941.
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    Citations

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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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