Random spherical hyperbolic diffusion

Brodbridge, Phil, Kolesnik, Alexander D., Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 and Olenko, Andriy 2019. Random spherical hyperbolic diffusion. Journal of Statistical Physics 177 (5) , pp. 889-916. 10.1007/s10955-019-02395-0

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Abstract

The paper starts by giving a motivation for this research and justifying the considered stochastic diffusion models for cosmic microwave background (CMB) radiation studies. Then it derives the exact solution in terms of a series expansion to a hyperbolic diffusion equation on the unit sphere. The Cauchy problem with random initial conditions is studied. All assumptions are stated in terms of the angular power spectrum of the initial conditions. An approximation to the solution is given and analysed by finitely truncating the series expansion. The upper bounds for the convergence rates of the approximation errors are derived. Smoothness properties of the solution and its approximation are investigated. It is demonstrated that the sample Hölder continuity of these spherical fields is related to the decay of the angular power spectrum. Numerical studies of approximations to the solution and applications to CMB data are presented to illustrate the theoretical results.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer Verlag (Germany)
ISSN:	0022-4715
Date of First Compliant Deposit:	12 September 2019
Date of Acceptance:	23 September 2019
Last Modified:	02 Dec 2024 14:30
URI:	https://orca.cardiff.ac.uk/id/eprint/125425

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