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On a class of space-time intrinsic random functions. (English) Zbl 1271.60062

Summary: Power-law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the degree of smoothness in space and in time may differ while maintaining other desirable properties for the covariance functions, including the availability of explicit convergent and asymptotic series expansions.

MSC:

60G60 Random fields
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
60G10 Stationary stochastic processes
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