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arXiv · 2112.02595

Characterization Theorems for Pseudo-Variograms

Christopher Dörr·Martin Schlather
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Abstract

Pseudo-variograms appear naturally in the context of multivariate Brown-Resnick processes, and are a useful tool for analysis and prediction of multivariate random fields. We give a necessary and sufficient criterion for a matrix-valued function to be a pseudo-variogram, and further provide a Schoenberg-type result connecting pseudo-variograms and multivariate correlation functions. By means of these characterizations, we provide extensions of the popular univariate space-time covariance model of Gneiting to the multivariate case.

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Christopher Dörr, Martin Schlather. 2021-12-05. Characterization Theorems for Pseudo-Variograms. https://arxiv.org/abs/2112.02595

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