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Theory of Probability and Mathematical Statistics

Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus

François Bachoc, Ana Paula Peron and Emilio Porcu


Abstract: The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the covariance functions, being in this case matrix valued mappings.

We start by considering the spectral representations that in turn allow for a characterization of such covariance functions. We then provide some methods for the construction of these matrix valued mappings. Finally, we consider strategies to evade radial symmetry (called isotropy in spatial statistics) and provide representation theorems for such a more general case.

Keywords: Matrix valued covariance functions, multivariate random fields, torus, matrix spectral density

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