In this article, we provide a comprehensive review of space–time covariance functions. As
for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit …

The last decades have seen an unprecedented increase in the availability of data sets that
are inherently global and temporally evolving, from remotely sensed networks to climate …

With the advent of wide-spread global and continental-scale spatiotemporal datasets,
increased attention has been given to covariance functions on spheres over time. This paper …

This survey contains a selection of topics unified by the concept of positive semidefiniteness
(of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or …

For quasi-metric spaces $(X,\rho) $ and $(Y,\sigma) $ and a positive real number $\lambda
$, we propose a model for generating positive definite functions $ G_r:\{\rho (x, x'): x, x'\in …

We present an explicit characterization for the real, continuous, isotropic and strictly positive
definite kernels on a product of compact two-point homogeneous spaces, covering almost …

The equivalence of Gaussian measures is a fundamental tool to establish the asymptotic
properties of both prediction and estimation of Gaussian fields under fixed domain …

The main contribution in the present paper is a characterization for positive definiteness and
strict positive definiteness of a kernel on the product X * S^ d X× S d, in which X is a …

We consider the class Ψ d of continuous functions that define isotropic covariance functions
in the d-dimensional sphere S d. We provide a new recurrence formula for the solution of …

The paper deals with multivariate Gaussian random fields defined over generalized product
spaces that involve the hypertorus. The assumption of Gaussianity implies the finite …