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Theory of Probability and Mathematical Statistics

Spatiotemporal covariance functions for Laplacian ARMA fields in higher dimensions

György H. Terdik


Abstract: This paper presents clear formulae of the covariance functions of Laplacian ARMA fields in terms of coefficients and Bessel functions in higher spatial dimensions. Spectral methods are used for the study of spatiotemporal Laplacian ARMA fields in Euclidean spaces and spheres therein with dimension d≥2.

Keywords: Isotropy, homogeneity, stationarity, space-time interaction, spectral density, Whittle–Matérn model, Laplacian ARMA fields in higher spatial dimensions, random fields on sphere

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