Isotropic Covariance Matrix Functions on Compact Two-Point Homogeneous Spaces

Tianshi Lu () and Chunsheng Ma ()
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Tianshi Lu: Wichita State University
Chunsheng Ma: Wichita State University

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1630-1656

Abstract: 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.

Keywords: Covariance matrix function; Elliptically contoured random field; Gaussian random field; Isotropy; Stationarity; Jacobi polynomial; Bessel function; 60G60; 62M10; 62M30 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-019-00920-1

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