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On spectral theory of random fields in the ball

journal contribution
posted on 2025-04-03, 22:47 authored by N Leonenko, A Malyarenko, Andriy OlenkoAndriy Olenko
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.

Funding

N. Leonenko and A. Olenko were partially supported under the Australian Research Council's Discovery Projects funding scheme (project number DP160101366).

History

Publication Date

2022-01-01

Journal

Theory of Probability and Mathematical Statistics

Volume

107

Pagination

16p. (p. 61-76)

Publisher

Taras Shevchenko National University of Kyiv and the American Mathematical Society

ISSN

0094-9000

Rights Statement

© 2022 Taras Shevchenko National University of Kyiv

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