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

Emilio Porcu; René L. Schilling

doi:10.3150/10-BEJ277

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

Emilio Porcu, René L. Schilling

Mathematics

Dresden University of Technology

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

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.

Original language	British English
Pages (from-to)	441-455
Number of pages	15
Journal	Bernoulli
Volume	17
Issue number	1
DOIs	https://doi.org/10.3150/10-BEJ277
State	Published - Feb 2011

Keywords

Complete Bernstein functions
Isotropy
Schoenberg-Lévy kernels
Variograms

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10.3150/10-BEJ277

Cite this

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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-L{\'e}vy type and demonstrate some important properties of rotationally invariant variograms.",

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AB - 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.

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

Abstract

Keywords

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