Isotropic Multiple Scattering Processes on Hyperspheres

This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres Sp-1. It allows one to derive the Fourier expansions on Sp-1 of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions on Sp-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 Sp-1 are obtained. Both Fourier expansion and asymptotic approximation allow us to compute estimation bounds for the parameters of compound cox processes on Sp-1.

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