Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type

Malyarenko, Anatoliy

doi:10.1007/bf02591915

Cited by 5 publications

(3 citation statements)

References 5 publications

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“…There is a trick that allows us to write down all zonal spherical functions of all compact two-point homogeneous spaces in the same form, which is used in probabilistic literature [2,28,25,26,33] and in approximation theory [9,13].…”

Section: A Geometric Approachmentioning

confidence: 99%

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Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

Malyarenko

2018

J Theor Probab

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A general form of the covariance matrix function is derived in this paper for a vector random field that is isotropic and mean square continuous on a compact connected two-point homogeneous space and stationary on a temporal domain. A series representation is presented for such a vector random field, which involve Jacobi polynomials and the distance defined on the compact two-point homogeneous space.

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Section: A Geometric Approachmentioning

confidence: 99%

“…See also surveys of the topic in the monographs [28,31,42,44]. Isotropic random fields on connected compact two-point homogeneous spaces are studied in [2,14,25,26,33], among others.…”

Section: Introductionmentioning

confidence: 99%

Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

Malyarenko

2018

J Theor Probab

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“…In this paper, we prove several theorems concerning relations between the asymptotic behavior of the spectral measure of random fields ξ(x) and η(x) at infinity and the asymptotic behavior of the variance of increments near zero. Other kinds of Abelian and Tauberian theorems for homogeneous and isotropic random fields are studied in [5,6,8,11,19].…”

Section: Definition 3 ([21])mentioning

confidence: 99%

Abelian and Tauberian theorems for random fields on two-point homogeneous spaces

Malyarenko

2005

Theor. Probability and Math. Statist.

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Abstract. We consider centered mean-square continuous random fields for which the variance of increments between two points depends only on the distance between these points. Relations between the asymptotic behavior of the variance of increments near zero and the asymptotic behavior of the spectral measure of the field near infinity are investigated. We prove several Abelian and Tauberian theorems in terms of slowly varying functions.

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Sample Path Properties of Gaussian Invariant Random Fields

Malyarenko

2013

Probability and Its Applications

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Local properties of gaussian random fields on compact symmetric spaces and theorems of the Jackson-Bernstein type

Cited by 5 publications

References 5 publications

Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

Time-Varying Isotropic Vector Random Fields on Compact Two-Point Homogeneous Spaces

Abelian and Tauberian theorems for random fields on two-point homogeneous spaces

Sample Path Properties of Gaussian Invariant Random Fields

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