Analysis of spherical monofractal and multifractal random fields

Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091, Nanayakkara, Ravindi and Olenko, Andryi 2021. Analysis of spherical monofractal and multifractal random fields. Stochastic Environmental Research and Risk Assessment 35 , pp. 681-701. 10.1007/s00477-020-01911-z

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag (Germany)
ISSN:	1436-3240
Date of First Compliant Deposit:	15 October 2020
Date of Acceptance:	16 October 2020
Last Modified:	20 Nov 2024 15:00
URI:	https://orca.cardiff.ac.uk/id/eprint/135665

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