Mathematical Genesis of the Spatio-Temporal Covariance Functions
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Copyright: © 2020 Gema Fernández-Avilés, Jose-María Montero and Jorge Mateu. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Problem statement: Obtaining new and flexible classes of nonseparable spatio-temporal covariances have resulted in a key point of research in the last years within the context of spatiotemporal Geostatistics. Approach: In general, the literature has focused on the problem of full symmetry and the problem of anisotropy has been overcome. Results: By exploring mathematical properties of positive definite functions and their close connection to covariance functions we are able to develop new spatio-temporal covariance models taking into account the problem of spatial anisotropy. Conclusion/Recommendations: The resulting structures are proved to have certain interesting mathematical properties, together with a considerable applicability.
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- Spatial anisotropy
- bernstein and complete monotone functions
- spatio-temporal Geostatistics
- positive definite functions
- space-time modeling
- spatio-temporal data