MULTIVARIATE GAUSSIAN RANDOM FIELDS OVER GENERALIZED PRODUCT SPACES INVOLVING THE HYPERTORUS

François Bachoc; Ana Paula Peron; Emilio Porcu

doi:10.1090/tpms/1176

MULTIVARIATE GAUSSIAN RANDOM FIELDS OVER GENERALIZED PRODUCT SPACES INVOLVING THE HYPERTORUS

François Bachoc, Ana Paula Peron, Emilio Porcu

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaus-sianity 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.

Original language	British English
Pages (from-to)	3-14
Number of pages	12
Journal	Theory of Probability and Mathematical Statistics
Volume	107
DOIs	https://doi.org/10.1090/tpms/1176
State	Published - 8 Nov 2022

Keywords

matrix spectral density
Matrix valued covariance functions
multivariate random fields
torus

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10.1090/tpms/1176

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abstract = "The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaus-sianity 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.",

keywords = "matrix spectral density, Matrix valued covariance functions, multivariate random fields, torus",

author = "Fran{\c c}ois Bachoc and Peron, {Ana Paula} and Emilio Porcu",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary 62M15, 62M30; Secondary 60G12. Key words and phrases. Matrix valued covariance functions, multivariate random fields, torus, matrix spectral density. 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. Publisher Copyright: {\textcopyright} 2022 Taras Shevchenko National University of Kyiv.",

year = "2022",

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doi = "10.1090/tpms/1176",

language = "British English",

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AU - Peron, Ana Paula

AU - Porcu, Emilio

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary 62M15, 62M30; Secondary 60G12. Key words and phrases. Matrix valued covariance functions, multivariate random fields, torus, matrix spectral density. 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. Publisher Copyright: © 2022 Taras Shevchenko National University of Kyiv.

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N2 - The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaus-sianity 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.

AB - The paper deals with multivariate Gaussian random fields defined over generalized product spaces that involve the hypertorus. The assumption of Gaus-sianity 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.

KW - matrix spectral density

KW - Matrix valued covariance functions

KW - multivariate random fields

KW - torus

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JF - Theory of Probability and Mathematical Statistics

ER -

MULTIVARIATE GAUSSIAN RANDOM FIELDS OVER GENERALIZED PRODUCT SPACES INVOLVING THE HYPERTORUS

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Keywords

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