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Characterization theorems for pseudo cross-variograms

Part of: Geophysics (general) Geophysics Stochastic processes

Published online by Cambridge University Press:  24 April 2023

Christopher Dörr  and
Martin Schlather
Christopher Dörr*
Affiliation:
University of Mannheim
Martin Schlather*
Affiliation:
University of Mannheim
*
*Postal address: Institute of Mathematics, University of Mannheim, 68131 Mannheim, Germany.
*Postal address: Institute of Mathematics, University of Mannheim, 68131 Mannheim, Germany.
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Abstract

Pseudo cross-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 cross-variogram, and further provide a Schoenberg-type result connecting pseudo cross-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.

Keywords

Multivariate geostatisticsconditionally negative definitepositive definitespace–time covariance functionsGneiting functions

MSC classification

Primary: 86A32: Geostatistics
Secondary: 60G10: Stationary processes
Type
Original Article
Information
Journal of Applied Probability , Volume 60 , Issue 4 , December 2023 , pp. 1219 - 1231
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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