Strict positive definiteness in geostatistics

  • S. De IacoEmail author
  • D. Posa
Original Paper


Geostatistical modeling is often based on the use of covariance functions, i.e., positive definite functions. However, when interpolation problems have to be solved, it is advisable to consider the subset of strictly positive definite functions. Indeed, it will be argued that ensuring strict positive definiteness for a covariance function is convenient from a theoretical and practical point of view. In this paper, an extensive analysis on strictly positive definite covariance functions has been given. The closure of the set of strictly positive definite functions with respect to the sum and the product of covariance functions defined on the same Euclidean dimensional space or on factor spaces, as well as on partially overlapped lower dimensional spaces, has been analyzed. These results are particularly useful (a) to extend strict positive definiteness in higher dimensional spaces starting from covariance functions which are only defined on lower dimensional spaces and/or are only strictly positive definite in lower dimensional spaces, (b) to construct strictly positive definite covariance functions in space–time as well as (c) to obtain new asymmetric and strictly positive definite covariance functions.


Strict positive definiteness Covariance functions Spatial dimension 



The authors would like to thank the associate editor, the reviewers and prof. Giorgio Metafune for their interest in the paper and their useful comments and suggestions.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Dipartimento di Scienze dell’EconomiaUniversità del SalentoLecceItaly
  2. 2.Dipartimento di Scienze Economiche e Matematico-StatisticheUniversità del SalentoLecceItaly

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