From Schoenberg to Pick-Nevanlinna: Toward a complete picture of the variogram class

Abstract

We show that a large subclass of variograms is closed under products and that some desirable stability properties, such as the product of special compositions, can be obtained within the proposed setting. We introduce new classes of kernels of Schoenberg-Lévy type and demonstrate some important properties of rotationally invariant variograms.

Published in at http://dx.doi.org/10.3150/10-BEJ277 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm). With Addendum

References in corpus (2)

• Stochastic models which separate fractal dimension and Hurst effect
• The Dagum family of isotropic correlation functions

Cited by in corpus (1)

• An exceptional max-stable process fully parameterized by its extremal coefficients