Student's t vector random fields with power-law and log-law decaying direct and cross covariances.

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Authors
Ma, Chunsheng
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Issue Date
2013-01-01
Type
Article
Keywords
Cauchy random field , Conditionally negative definite matrix , Covariance matrix function , Elliptically contoured random field , Gaussian random field , Long range dependence , Spherically invariant random field , Stable random field , Variogram , 60G12 , 60G22 , 60G15 , 60G60 , 60G18
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Ma, Chunsheng. 2013. Student's t vector random fields with power-law and log-law decaying direct and cross covariances. Stochastic Analysis and Applications, v.31 no.1 pp.167-182
Abstract

This article deals with the Student's t vector random field, which is formulated as a scale mixture of Gaussian vector random fields, and whose finite-dimensional distributions decay in power-law and have heavy tails. There are two classes of Student's t vector random fields, one with second-order moments, and the other without a second-order moment. A Cauchy vector random field is an example of Student's t vector random fields without a first-order moment, and is also an example of Stable vector random fields. A second-order Student's t vector random field allows for any given correlation structure, just as a Gaussian vector random field does. We propose four types of covariance matrix structures for second-order Student's t vector random fields, which decay in power-law or log-law.

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Publisher
Taylor & Francis, Inc
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Series
Stochastic Analysis and Applications;v.31 no.1
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DOI
ISSN
0736-2994
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