Isotropic covariance matrix functions on compact two-point homogeneous spaces

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Authors
Lu, Tianshi
Ma, Chunsheng
Issue Date
2019
Type
Article
Language
en_US
Keywords
Bessel function , Covariance matrix function , Elliptically contoured random field , Gaussian random field , Isotropy , Jacobi polynomial , Stationarity
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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.

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Citation
Lu, T. & Ma, C. J Theor Probab (2019)
Publisher
Springer
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ISSN
0894-9840
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