Convergence arguments to bridge cauchy and matérn covariance functions

Tarik Faouzi, Emilio Porcu, Igor Kondrashuk, Moreno Bevilacqua

Research output: Contribution to journalArticlepeer-review


The Matérn 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 Matérn 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 Matérn family, providing a somewhat surprising bridge between covariance models with light tails and covariance models that allow for long memory effect.

Original languageBritish English
JournalStatistical Papers
StateAccepted/In press - 2023


  • Mellin–Barnes transforms
  • Positive definite
  • Random field
  • Spectral densities


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