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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



Multivariate Gaussian Random Fields over Generalized Product Spaces involving the Hypertorus

Authors: François Bachoc, Ana Paula Peron and Emilio Porcu
Journal: Theor. Probability and Math. Statist. 107 (2022), 3-14
MSC (2020): Primary 62M15, 62M30; Secondary 60G12
Published electronically: November 8, 2022
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Abstract | References | Similar Articles | Additional Information


The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaussianity implies the finite dimensional distributions to be completely specified by the covariance functions, being in this case matrix valued mappings.

We start by considering the spectral representations that in turn allow for a characterization of such covariance functions. We then provide some methods for the construction of these matrix valued mappings. Finally, we consider strategies to evade radial symmetry (called isotropy in spatial statistics) and provide representation theorems for such a more general case.

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Additional Information

François Bachoc
Affiliation: Department of Mathematics, Université Paul Sabatier, Toulouse, France.

Ana Paula Peron
Affiliation: Department of Mathematics, ICMC, University of São Paulo, São Carlos, Brazil.

Emilio Porcu
Affiliation: Department of Mathematics, Khalifa University, The United Arab Emirates, $\&$ School of Computer Science and Statistics, Trinity College Dublin.

Keywords: Matrix valued covariance functions, multivariate random fields, torus, matrix spectral density
Received by editor(s): June 9, 2021
Accepted for publication: November 15, 2021
Published electronically: November 8, 2022
Additional Notes: A. P. Peron was partially supported by FAPESP # 2021/04269-0.
E. Porcu acknowledges this publication is based upon work supported by the Khalifa University of Science and Technology under Award No. FSU-2021-016
Dedicated: This paper is dedicated to Professor M. Yadrenko, who has largely inspired our research since the times of our PhD studies.
Article copyright: © Copyright 2022 Taras Shevchenko National University of Kyiv