Gneiting Class, Semi-Metric Spaces and Isometric Embeddings

Year 2020, Volume: 3 Issue: 2, 85 - 95, 01.06.2020

Valdir Menegatto Claudemir Oliveira Emilio Porcu

https://doi.org/10.33205/cma.712049

Cited By: 5

Abstract

This paper revisits the Gneiting class of positive definite kernels originally proposed as a class of covariance functions for space-time processes.\ Under the framework of quasi-metric spaces and isometric embeddings, the paper proposes a general and unifying framework that encompasses results provided by earlier literature.\ Our results allow to study the positive definiteness of the Gneiting class over products of either Euclidean spaces or high dimensional spheres and quasi-metric spaces.\ In turn, Gneiting's theorem is proved here by a direct construction, eluding Fourier inversion (the so-called Gneiting's lemma) and convergence arguments that are required by Gneiting to preserve an integrability assumption.

Keywords

Gneiting class, positive definite, completely monorone, isometric embedding

Supporting Institution

None

Project Number

Nove

Thanks

Void

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