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Addendum to ‘Isotropic correlation functions on d-dimensional balls’

Part of: Geophysics Geophysics (general) Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Tilmann Gneiting
Tilmann Gneiting*
Affiliation:
University of Washington
*
∗ Postal address: Department of Statistics, Box 354322, University of Washington, Seattle, WA 98195-4322, USA. Email address: tilmann@stat.washington.edu
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Abstract

We discuss necessary and sufficient conditions for power-law and polynomial models to be correlation functions on bounded domains. These results date back to unpublished work by Matheron (1974) and generalize the findings of Gneiting (1999).

Keywords

Covariance functiongeostatisticspositive definite

MSC classification

Primary: 86A32: Geostatistics
Secondary: 60G60: Random fields
Type
Stochastic Geometry and Statistical Applications
Information
Advances in Applied Probability , Volume 32 , Issue 4 , December 2000 , pp. 960 - 961
Copyright
Copyright © Applied Probability Trust 2000 

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References

Chilès, J.-P. and Delfiner, P. (1999). Geostatistics. Modeling Spatial Uncertainty. John Wiley, New York.CrossRefGoogle Scholar
Gneiting, T. (1999). Isotropic correlation functions on d-dimensional balls. Adv. Appl. Prob. 31, 625–631.CrossRefGoogle Scholar
Matheron, G. (1973). The intrinsic random functions and their applications. Adv. Appl. Prob. 5, 439–468.CrossRefGoogle Scholar
Matheron, G. (1974). Représentations stationnaires et représentations minimales pour les FAI-k. Note Géostatistique 125, Centre de Géostatistique, Fontainebleau, France.Google Scholar