On Spectral Theory of Random Fields in the Ball
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Publication:6373997
DOI10.1090/TPMS/1175zbMATH Open1515.60157arXiv2107.13691MaRDI QIDQ6373997
Anatoliy Malyarenko, Nikolai N. Leonenko, Andriy Olenko
Publication date: 28 July 2021
Abstract: The paper investigates random fields in the ball. It studies three types of such fields: restrictions of scalar random fields in the ball to the sphere, spin, and vector random fields. The review of the existing results and new spectral theory for each of these classes of random fields are given. Examples of applications to classical and new models of these three types are presented. In particular, the Mat'{e}rn model is used for illustrative examples. The derived spectral representations can be utilised to further study theoretical properties of such fields and to simulate their realisations. The obtained results can also find various applications for modelling and investigating ball data in cosmology, geosciences and embryology.
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