  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 ${\mathbb S}^{p-1}$.
