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Time Varying Isotropic Vector Random Fields on Spheres

Author

Listed:
  • Chunsheng Ma

    (Wichita State University
    Wuhan University of Technology
    Hubei Engineering University)

Abstract

For a vector random field that is isotropic and mean square continuous on a sphere and stationary on a temporal domain, this paper derives a general form of its covariance matrix function and provides a series representation for the random field, which involve the ultraspherical polynomials. The series representation is somehow an imitator of the covariance matrix function, but differs from the spectral representation in terms of the ordinary spherical harmonics, and is useful for modeling and simulation. Some semiparametric models are also illustrated.

Suggested Citation

  • Chunsheng Ma, 2017. "Time Varying Isotropic Vector Random Fields on Spheres," Journal of Theoretical Probability, Springer, vol. 30(4), pages 1763-1785, December.
    • Handle: RePEc:spr:jotpro:v:30:y:2017:i:4:d:10.1007_s10959-016-0689-1
    DOI: 10.1007/s10959-016-0689-1
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    References listed on IDEAS

    as
    1. 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.
    2. Roch Roy, 1976. "Spectral analysis for a random process on the sphere," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 91-97, December.
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    Cited by:

    1. 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.
    2. Bingham, Nicholas H. & Symons, Tasmin L., 2022. "Gaussian random fields on the sphere and sphere cross line," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 788-801.
    3. 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.
    4. 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.

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