Isotropic covariance matrix polynomials on spheres

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Authors
Ma, Chunsheng
Issue Date
2016
Type
Article
Language
en_US
Keywords
Covariance matrix function , Elliptically contoured vector random field , Gaussian vector random field , Gegenbauer polynomial , Positive definite , Ultraspherical expansion , 60G10 , 60G15 , 60G60 , 62M30
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Abstract

This article characterizes the covariance matrix function of a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the sphere. By applying the characterization to examine the validity of a matrix function whose entries are polynomials of degrees up to 4, we obtain a necessary and sufficient condition for the polynomial matrix to be an isotropic covariance matrix function on the sphere.

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Citation
Ma, Chunsheng. Isotropic covariance matrix polynomials on spheres. Stochastic Analysis and Applications, vol. 34:no. 4:pp 679-706
Publisher
Taylor & Francis Group
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ISSN
0736-2994
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