Construction of non-Gaussian random fields with any given correlation structure
Ma, Chunsheng
Ma, Chunsheng
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2009-03-01
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Covariance function,Elliptically contoured random field,Gaussian random field,Negative definite,Positive definite,Second-order random field,Variogram
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Chunsheng Ma, Construction of non-Gaussian random fields with any given correlation structure, Journal of Statistical Planning and Inference, Volume 139, Issue 3, 2009, Pages 780-787, ISSN 0378-3758, https://doi.org/10.1016/j.jspi.2008.03.043.
Abstract
A positive definite function can be thought of as the covariance function of a Gaussian random field, according to the celebrated Kolmogorov existence theorem. A question of great theoretical and practical interest is: how could one construct a non-Gaussian random field with the given positive definite function as its covariance function? In this paper we demonstrate a novel and simple method for constructing many such non-Gaussian random fields, with the corresponding finite-dimensional distributions identified. Also, we show how to construct a non-Gaussian random field with a given negative definite function as its variogram. © 2008 Elsevier B.V. All rights reserved.
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Elsevier B.V.
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Journal of Statistical Planning and Inference
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03783758