Research Article Open Access

Mathematical Genesis of the Spatio-Temporal Covariance Functions

Gema Fernández-Avilés1, Jose-María Montero1 and Jorge Mateu2
  • 1 , Afganistan
  • 2 ,
Journal of Mathematics and Statistics
Volume 7 No. 1, 2011, 37-44

DOI: https://doi.org/10.3844/jmssp.2011.37.44

Submitted On: 23 September 2010 Published On: 31 January 2011

How to Cite: Fernández-Avilés, G., Montero, J. & Mateu, J. (2011). Mathematical Genesis of the Spatio-Temporal Covariance Functions. Journal of Mathematics and Statistics, 7(1), 37-44. https://doi.org/10.3844/jmssp.2011.37.44

Abstract

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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Keywords

  • Spatial anisotropy
  • bernstein and complete monotone functions
  • spatio-temporal Geostatistics
  • positive definite functions
  • space-time modeling
  • spatio-temporal data