On Spectral Representations of Tensor Random Fields on the Sphere

Leonenko, Nikolai; Sakhno, Lyudmyla

doi:10.1080/07362994.2012.628912

Cited by 33 publications

(34 citation statements)

References 32 publications

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“…These models have received recently much attention (see [10], [12] or [14]), being motivated by the modeling of CMB data. Actually our point of view begins from [12].…”

Section: Random Sections Of Vector Bundlesmentioning

confidence: 99%

“…There are different approaches to the theory of random sections of homogeneous line bundles on S 2 (see [8], [10], [12], [16] e.g. ).…”

Section: The Connection With Classical Spin Theorymentioning

confidence: 99%

“…Moreover thanks to the ESA satellite Planck mission, new data concerning the polarization of the CMB will soon be available and the modeling of this quantity has led quite naturally to the investigation of spin random fields on S 2 , a subject that has already received much attention (see [8], [10], [12] and again [14] chapter 12 e.g. ).…”

Section: Introductionmentioning

confidence: 99%

“…They are equivalent but we did not find a formal proof of this equivalence. So §8 is devoted to the comparison with other constructions ( [8], [10], [12], [16]). In particular we show that the construction of spin random fields on S 2 of [8] is actually equivalent to ours, the difference being that their point of view is based on an accurate description of local charts and transition functions, instead of our more global perspective.…”

Section: Introductionmentioning

confidence: 99%

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Representation of Gaussian isotropic spin random fields

Baldi

Rossi

2014

Stochastic Processes and their Applications

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We develop a technique for the construction of random fields on algebraic structures. We deal with two general situations: random fields on homogeneous spaces of a compact group and in the spin line bundles of the 2-sphere. In particular, every complex Gaussian isotropic spin random field can be represented in this way. Our construction extends P. Lévy's original idea for the spherical Brownian motion.

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“…These models have received recently much attention (see [10], [12] or [14]), being motivated by the modeling of CMB data. Actually our point of view begins from [12].…”

Section: Random Sections Of Vector Bundlesmentioning

confidence: 99%

“…There are different approaches to the theory of random sections of homogeneous line bundles on S 2 (see [8], [10], [12], [16] e.g. ).…”

Section: The Connection With Classical Spin Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Representation of Gaussian isotropic spin random fields

Baldi

Rossi

2014

Stochastic Processes and their Applications

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“…Finally, in Appendices we shortly describe the mathematical terminology which is not always familiar to specialists in probability: tensors, group representations, and classical invariant theory. For different aspects of theory of random fields see also [24,25].…”

Section: Definition 3 ([17]) a Homogeneous And Isotropic Random Fieldmentioning

confidence: 99%

Matérn Class Tensor-Valued Random Fields and Beyond

Leonenko

Malyarenko

2017

J Stat Phys

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We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of 3 × 3 orthogonal matrices. The constructed classes depend on finitely many isotropic spectral densities. We say that such a field belongs to either the Matérn or the dual Matérn class if all of the above densities are Matérn or dual Matérn. Several examples are considered.

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30 Years of space–time covariance functions

Porcu

Furrer

Nychka

2020

WIREs Computational Stats

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In this article, we provide a comprehensive review of space–time covariance functions. As for the spatial domain, we focus on either the d‐dimensional Euclidean space or on the unit d‐dimensional sphere. We start by providing background information about (spatial) covariance functions and their properties along with different types of covariance functions. While we focus primarily on Gaussian processes, many of the results are independent of the underlying distribution, as the covariance only depends on second‐moment relationships. We discuss properties of space–time covariance functions along with the relevant results associated with spectral representations. Special attention is given to the Gneiting class of covariance functions, which has been especially popular in space–time geostatistical modeling. We then discuss some techniques that are useful for constructing new classes of space–time covariance functions. Separate treatment is reserved for spectral models, as well as to what are termed models with special features. We also discuss the problem of estimation of parametric classes of space–time covariance functions. An outlook concludes the paper. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Multivariate Analysis

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On Spectral Representations of Tensor Random Fields on the Sphere

Cited by 33 publications

References 32 publications

Representation of Gaussian isotropic spin random fields

Representation of Gaussian isotropic spin random fields

Matérn Class Tensor-Valued Random Fields and Beyond

30 Years of space–time covariance functions

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