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

DOI10.3150/10-BEJ277zbMath1280.60032arXiv0812.2936OpenAlexW3103367098MaRDI QIDQ637110

Emilio Porcu, Rene L. Schilling

Publication date: 2 September 2011

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.2936

zbMATH Keywords

isotropyvariogramscomplete Bernstein functionsSchoenberg-Lévy kernels

Mathematics Subject Classification ID

Random fields (60G60) Random fields; image analysis (62M40) Gaussian processes (60G15) Stationary stochastic processes (60G10) Characteristic functions; other transforms (60E10)

Related Items (13)

Criteria and characterizations for spatially isotropic and temporally symmetric matrix-valued covariance functions ⋮ Extending the Gneiting class for modeling spatially isotropic and temporally symmetric vector random fields ⋮ New validity conditions for the multivariate Matérn coregionalization model, with an application to exploration geochemistry ⋮ Modeling Temporally Evolving and Spatially Globally Dependent Data ⋮ Covariance models for multivariate random fields resulting from pseudo cross-variograms ⋮ Spherical process models for global spatial statistics ⋮ Addendum to ``From Schoenberg to Pick-Nevanlinna: towards a complete picture of the variogram class ⋮ Characterization theorems for some classes of covariance functions associated to vector valued random fields ⋮ Anisotropy models for spatial data ⋮ On subordination of holomorphic semigroups ⋮ Bringing order to rankings of utility functions by strong increases in \(n\)th order aversion to risk ⋮ Towards a complete picture of stationary covariance functions on spheres cross time ⋮ An exceptional max-stable process fully parameterized by its extremal coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Function spaces as Dirichlet spaces (about a paper by Maz'ya and Nagel)
• The Dagum family of isotropic correlation functions
• Quasi-arithmetic means of covariance functions with potential applications to space-time data
• Spatial variation. 2nd ed
• Interpolation of spatial data. Some theory for kriging
• Fractional Brownian sheet
• Summations for basic hypergeometric series involving a \(q\)-analogue of the digamma function
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• A new majorization between functions, polynomials, and operator inequalities
• Fonctions operant sur les fonctions definies-négatives
• Sur une demonstration de la formule de Levy-Kinchine
• Spherical distributions: Schoenberg (1938) revisited
• Criteria of Pólya type for radial positive definite functions
• Why is isotropy so prevalent in spatial statistics?
• Classes of infinitely divisible distributions and densities
• A convolution equation relating the generalized Γ-convolutions and the Bondesson Class
• The intrinsic random functions and their applications
• Stochastic Models That Separate Fractal Dimension and the Hurst Effect
• Isotropic correlation functions on d-dimensional balls
• Metric Spaces and Positive Definite Functions
• Bernstein functions. Theory and applications

This page was built for publication: From Schoenberg to Pick-Nevanlinna: toward a complete picture of the variogram class