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