Abstract : This paper presents several results about isotropic random walks and multiple scattering processes on hyperspheres S p−1. It allows one to derive the Fourier expansions on S p−1 of these processes. A result of unimodality for the multiconvolution of symmetrical probability density functions (pdf) on 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 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 S p−1. Index Terms Isotropic random walk on S p−1 , Compound Cox Processes on S p−1 , von Mises-Fisher distribution, Fourier series expansion on hyperspheres, multiple scattering, Cramer-Rao lower bounds.