Space-time covariance functions with compact support

TL;DR

This paper characterizes the Gneiting class of space-time covariance functions, relaxes conditions for their construction, and explores criteria for compact support in multivariate Gaussian fields, advancing spatial statistics theory.

Contribution

It provides a complete characterization of the Gneiting class, relaxes construction conditions, and establishes necessary criteria for compact support in multivariate Gaussian fields.

Findings

Necessary conditions for compactly supported Gneiting functions.

Relaxed conditions on functions defining space-time covariance.

Criteria for generators of multivariate Gaussian fields to be compactly supported.

Abstract

We characterize completely the Gneiting class of space-time covariance functions and give more relaxed conditions on the involved functions. We then show necessary conditions for the construction of compactly supported functions of the Gneiting type. These conditions are very general since they do not depend on the Euclidean norm. Finally, we discuss a general class of positive definite functions, used for multivariate Gaussian random fields. For this class, we show necessary criteria for its generator to be compactly supported.