Stochastic representations of isotropic vector random fields on spheres

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Authors
Ma, Chunsheng
Advisors
Issue Date
2016
Type
Article
Keywords
Covariance matrix function , Cross covariance , Direct covariance , Elliptically contoured random field , Funk-Hecke formula , Gaussian random field , Gegenbauers polynomials
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Citation
Ma, Chunsheng. 2016. Stochastic representations of isotropic vector random fields on spheres. Stochastic Analysis and Applications, vol. 34:no. 3:pp 389-403
Abstract

A stochastic representation is derived for a vector random field that is stationary, isotropic, and mean square continuous on a sphere or unit circle. The established stochastic representation is an infinite series involving the sequence of ultraspherical or Gegenbauer's polynomials, looks like a mimic of the series representation of the covariance matrix function of the isotropic vector random field, but differs from the spectral representation in terms of the ordinary spherical harmonics. It is also shown in this paper that some isotropic and continuous covariance matrix functions on the real line or R-3, if they are compactly supported, can be adopted as covariance matrix functions on the unit circle or S-3.

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Publisher
Taylor & Francis Group
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Book Title
Series
Stochastic Analysis and Applications;v.34:no.3
PubMed ID
DOI
ISSN
0736-2994
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