Mat\'{e}rn Class Tensor-Valued Random Fields and Beyond

Nikolai Leonenko; Anatoliy Malyarenko

doi:10.1007/s10955-017-1847-2

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arXiv · 1701.07345

Mat\'{e}rn Class Tensor-Valued Random Fields and Beyond

Nikolai Leonenko·Anatoliy Malyarenko

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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 Mat\'{e}rn or the dual Mat\'{e}rn class if all of the above densities are Mat\'{e}rn or dual Mat\'{e}rn. Several examples are considered.

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Nikolai Leonenko, Anatoliy Malyarenko. 2017-01-25. Mat\'{e}rn Class Tensor-Valued Random Fields and Beyond. https://doi.org/10.1007/s10955-017-1847-2

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