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Matérn Class Tensor-Valued Random Fields and Beyond
Nikolai Leonenko, Anatoliy Malyarenko · 2017-01-25 · via math.PR updates on arXiv.org

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.

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