Regularity properties and simulations of Gaussian random fields on the sphere cross time

We study the regularity properties of Gaussian fields defined over spheres across time. In particular, we consider two alternative spectral decompositions for a Gaussian field on S d × R. For each decomposition, we establish regularity properties through Sobolev and interpolation spaces. We then pro...

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Bibliographic Details
Published inElectronic journal of statistics Vol. 12; no. 1
Main Authors Clarke De la Cerda, Jorge, Alegría, Alfredo, Porcu, Emilio
Format Journal Article
LanguageEnglish
Published Shaker Heights, OH : Institute of Mathematical Statistics 01.01.2018
Subjects
Mathematics
Probability
Statistics
Space-time covariance
Schoenberg's functions
Global data
Karhunen-Lóeve expansion
Big data
Gaussian random fields
Spherical harmonics functions
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Summary:We study the regularity properties of Gaussian fields defined over spheres across time. In particular, we consider two alternative spectral decompositions for a Gaussian field on S d × R. For each decomposition, we establish regularity properties through Sobolev and interpolation spaces. We then propose a simulation method and study its level of accuracy in the L 2 sense. The method turns to be both fast and efficient.
ISSN:1935-7524
1935-7524
DOI:10.1214/18-EJS1393