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Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces

Author

Listed:
  • Cleanthous, Galatia
  • Georgiadis, Athanasios G.
  • Lang, Annika
  • Porcu, Emilio

Abstract

Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided.

Suggested Citation

  • Cleanthous, Galatia & Georgiadis, Athanasios G. & Lang, Annika & Porcu, Emilio, 2020. "Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4873-4891.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:8:p:4873-4891
    DOI: 10.1016/j.spa.2020.02.003
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    References listed on IDEAS

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    1. Emilio Porcu & Alfredo Alegria & Reinhard Furrer, 2018. "Modeling Temporally Evolving and Spatially Globally Dependent Data," International Statistical Review, International Statistical Institute, vol. 86(2), pages 344-377, August.
    2. 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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    Cited by:

    1. Galatia Cleanthous & Emilio Porcu & Philip White, 2021. "Regularity and approximation of Gaussian random fields evolving temporally over compact two-point homogeneous spaces," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 836-860, December.

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