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arXiv · 1408.2887

Isotropic Multiple Scattering Processes on Hyperspheres

Nicolas Le Bihan·Florent Chatelain·Jonathan H. Manton
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Abstract

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres ${\mathbb S}^{p-1}$. It allows one to derive the Fourier expansions on ${\mathbb S}^{p-1}$ of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on ${\mathbb S}^{p-1}$ is also introduced. Such processes are then studied in the case where the scattering distribution is von Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs on ${\mathbb S}^{p-1}$ are obtained. Both Fourier expansion and asymptotic approximation allows us to compute estimation bounds for the parameters of Compound Cox Processes (CCP) on ${\mathbb S}^{p-1}$.

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Nicolas Le Bihan, Florent Chatelain, Jonathan H. Manton. 2014-08-13. Isotropic Multiple Scattering Processes on Hyperspheres. https://arxiv.org/abs/1408.2887

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