Correlation Structures

Anatoliy Malyarenko; Martin Ostoja-Starzewski; Amirhossein Amiri-Hezaveh

doi:10.1007/978-3-030-60064-8_4

Correlation Structures

Anatoliy Malyarenko, Martin Ostoja-Starzewski, Amirhossein Amiri-Hezaveh

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We calculate the one- and two-point correlation tensors of a homogeneous and (K, θ) -isotropic random field, where K is one of the 10 closed subgroups of the group O (3 ) lying between the group D₂ and its normaliser, O×Z2c, and where θ is the restriction of the natural representation of the group K in the space of all piezoelectric tensors to the 3-dimensional linear space where the group D₂ acts trivially. The spectral expansion of such a field in terms of stochastic integrals with respect to certain random measures is also calculated.

Original language	English (US)
Title of host publication	SpringerBriefs in Applied Sciences and Technology
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	41-91
Number of pages	51
DOIs	https://doi.org/10.1007/978-3-030-60064-8_4
State	Published - 2020

Publication series

Name	SpringerBriefs in Applied Sciences and Technology
ISSN (Print)	2191-530X
ISSN (Electronic)	2191-5318

ASJC Scopus subject areas

Biotechnology
Chemical Engineering(all)
Mathematics(all)
Materials Science(all)
Energy Engineering and Power Technology
Engineering(all)

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10.1007/978-3-030-60064-8_4

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AU - Amiri-Hezaveh, Amirhossein

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AB - We calculate the one- and two-point correlation tensors of a homogeneous and (K, θ) -isotropic random field, where K is one of the 10 closed subgroups of the group O (3 ) lying between the group D2 and its normaliser, O×Z2c, and where θ is the restriction of the natural representation of the group K in the space of all piezoelectric tensors to the 3-dimensional linear space where the group D2 acts trivially. The spectral expansion of such a field in terms of stochastic integrals with respect to certain random measures is also calculated.

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