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