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  • 1.
    Leonenko, Nikolai
    et al.
    Cardiff University, UK.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Matérn Class Tensor-Valued Random Fields and Beyond2017In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 168, p. 1276-1301Article in journal (Refereed)
    Abstract [en]

    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 × 3 orthogonal matrices.The constructed classes depend on finitely many isotropic spectral densities. We say that such a field belongs 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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