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Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)



On spectral theory of random fields in the ball

Authors: Nikolai Leonenko, Anatoliy Malyarenko and Andriy Olenko
Journal: Theor. Probability and Math. Statist. 107 (2022), 61-76
MSC (2020): Primary 60G60, 60G15
Published electronically: November 8, 2022
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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 Matérn 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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Additional Information

Nikolai Leonenko
Affiliation: School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK

Anatoliy Malyarenko
Affiliation: Division of Mathematics and Physics, Mälardalen University, 721 23 Västerås, Sweden

Andriy Olenko
Affiliation: Department of Mathematics and Statistics, La Trobe University, Melbourne, VIC 3086, Australia

Keywords: Random fields, spectral theory, spin, isotropic, random fields in the ball, spherical random fields, Matérn covariance
Received by editor(s): July 29, 2021
Accepted for publication: November 11, 2021
Published electronically: November 8, 2022
Additional Notes: N. Leonenko and A. Olenko were partially supported under the Australian Research Council’s Discovery Projects funding scheme (project number DP160101366).
Dedicated: The paper is dedicated to the 90th birth anniversary of Professor Myhailo Yosypovych Yadrenko (1932–2004).
Article copyright: © Copyright 2022 Taras Shevchenko National University of Kyiv