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arXiv · 2207.11891

Convergence Arguments to Bridge Cauchy and Mat\'ern Covariance Functions

Tarik Faouzi·Emilio Procu·Igor Kondrashuk·Moreno Bevilacqua
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Abstract

The Mat\'ern and the Generalized Cauchy families of covariance functions have a prominent role in spatial statistics as well as in a wealth of statistical applications. The Mat\'ern family is crucial to index mean-square differentiability of the associated Gaussian random field; the Cauchy family is a decoupler of the fractal dimension and Hurst effect for Gaussian random fields that are not self-similar. Our effort is devoted to prove that a scale-dependent family of covariance functions, obtained as a reparameterization of the Generalized Cauchy family, converges to a particular case of the Mat\'ern family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.

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Tarik Faouzi, Emilio Procu, Igor Kondrashuk, Moreno Bevilacqua. 2022-07-25. Convergence Arguments to Bridge Cauchy and Mat\'ern Covariance Functions. https://doi.org/10.1007/s00362-023-01400-9

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