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Time varying axially symmetric vector random fields on the sphere. (English) Zbl 1353.60048
Summary: This paper presents a general form of the covariance matrix structure for a vector random field that is axially symmetric and mean square continuous on the sphere and provides a series representation for a longitudinally reversible one. The series representation is somehow an imitator of the covariance matrix function, and both of them have simpler forms than those proposed in the literature in terms of the associated Legendre functions and are useful for modeling and simulation. Also, a general form of the covariance matrix structure is derived for a spatio-temporal vector random field that is axially symmetric and mean square continuous over the sphere, and a series representation is given for a longitudinally reversible one.

MSC:
60G60 Random fields
60G15 Gaussian processes
62M40 Random fields; image analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M30 Inference from spatial processes
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