Matérn Class Tensor-Valued Random Fields and Beyond

Abstract

We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are isotropic with respect to a fixed orthogonal representation of the group of $3\times 3$ orthogonal matrices. The constructed classes depend on finitely many isotropic spectral densities. We say that such a field belong to either the Matérn or the dual Matérn class if all of the above densities are Matérn or dual Matérn. Several examples are considered.

37 pages, no figures

References in corpus (2)

• Cross-Covariance Functions for Multivariate Geostatistics
• A random field formulation of Hooke's law in all elasticity classes

Cited by in corpus (1)

• Convergence Arguments to Bridge Cauchy and Matérn Covariance Functions