Construction of non-Gaussian random fields with any given correlation structure |
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Authors: | Chunsheng Ma |
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Affiliation: | Department of Mathematics and Statistics, Wichita State University, KS 67260-0033, USA |
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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. |
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Keywords: | 60G12 60G15 60G60 62M30 42A82 |
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