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Hole-Effect Correlation Models Generalizing Matern and Generalized Wendland
Two parametric families of isotropic correlation functions for Gaussian random fields that, unlike most standard models, can take negative values (hole effects) while still parameterizing smoothness and global or compact support. They are built by iteratively applying the turning-bands operator to the Matern and Generalized Wendland models, which are recovered as special cases, with closed-form expressions for important cases and a proven limiting link showing a reparameterized hole-effect Generalized Wendland includes the hole-effect Matern as a limit.