Hyperbolic vector random fields with hyperbolic direct and cross covariance functions
Du, Juan Leonenko, Nikolai N. Ma, Chunsheng Shu, Hong
Du, Juan
Leonenko, Nikolai N.
Ma, Chunsheng
Shu, Hong
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2012-06-26
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Article
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Conditionally negative definite matrix,Covariance matrix function,Elliptically contoured random field,Gaussian random field,Generalized hyperbolic distribution,Generalized inverse Gaussian distribution,Spherically invariant random field,Variogram
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Du, Juan; Leonenko, Nikolai; Ma, Chunsheng & Hong, Shu.2012. Hyperbolic vector random fields with hyperbolic direct and cross covariance functions, Stochastic Analysis and Applications, Volume 30, Issue 4, pp.662-674
Abstract
This article introduces the hyperbolic vector random field whose finite-dimensional distributions are the generalized hyperbolic one, which is formulated as a scale mixture of Gaussian random fields and is thus an elliptically contoured (or spherically invariant) random field. Such a vector random field may or may not have second-order moments, while a second-order one is characterized by its mean function and its covariance matrix function, just as in a Gaussian case. Some covariance matrix structures of hyperbolic type are constructed in this paper for second-order hyperbolic vector random fields.
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Taylor & Francis
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Stochastic Analysis and Applications;2012, Vol.30, No.4
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0736-2994