Criteria and characterizations for spatially isotropic and temporally symmetric matrix-valued covariance functions

Emilio Porcu, Xavier Emery, Nadia Mery

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider spatial matrix-valued isotropic covariance functions in Euclidean spaces and provide a very short proof of a celebrated characterization result proposed by earlier literature. We then provide a characterization theorem to create a bridge between a class of matrix-valued functions and the class of matrix-valued positive semidefinite functions in finite-dimensional Euclidean spaces. We culminate with criteria of the Pólya type for matrix-valued isotropic covariance functions, and with a generalization of Schlather’s class of multivariate spatial covariance functions. We then challenge the problem of matrix-valued space–time covariance functions, and provide a general class that encompasses all the proposals on the Gneiting nonseparable class provided by earlier literature.

Original languageBritish English
Article number223
JournalComputational and Applied Mathematics
Volume41
Issue number5
DOIs
StatePublished - Jul 2022

Keywords

  • Completely monotone matrix-valued functions
  • Multiply monotone matrix-valued functions
  • Multivariate Gneiting covariance
  • Positive semidefinite matrix-valued functions

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