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Analysis of spherical monofractal and multifractal random fields

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posted on 2025-03-31, 03:21 authored by Nikolai Leonenko, Ravindi NanayakkaraRavindi Nanayakkara, Andriy OlenkoAndriy Olenko
The Rényi function plays an important role in the analysis of multifractal random fields. For random fields on the sphere, there are three models in the literature where the Rényi function is known explicitly. The theoretical part of the article presents multifractal random fields on the sphere and develops specific models where the Rényi function can be computed explicitly. For all considered models explicit expressions of their multifractal spectrum are obtained. Properties of the models and dependencies of their characteristics on parameters are investigated. Then these results are applied to the Cosmic Microwave Background Radiation data collected from the Planck mission. The main statistical model used to describe these data in the literature is isotropic Gaussian fields. We present numerical multifractality studies and methodology based on simulating random fields, computing the Rényi function and the multifractal spectrum for different scenarios and actual CMB data. The obtained results can also find numerous potential applications for other geoscience, environmental and directional data.

Funding

This research was partially supported under the Australian Research Council’s Discovery Projects funding scheme (Project Number DP160101366).

History

Publication Date

2021-03-01

Journal

Stochastic Environmental Research and Risk Assessment

Volume

35

Pagination

21p. (p. 681-701)

Publisher

Springer Nature

ISSN

1436-3240

Rights Statement

© Springer-Verlag GmbH Germany, part of Springer Nature, 2020. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00477-020-01911-z

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