In this paper we consider isotropic processes on a homogeneous tree of order q, i.e. stochastic processes which covariance function depends only on the distance on the tree. We develop a characterization of isotropic processes via a reflection coefficient sequence. The relation between the covariance sequence and the reflection coefficient sequence of a process is derived by generalized Levinson and Schur recursions respectively . Although these results are easily obtained using an isometric (i.e. non-oriented) approach, the Levinson and Schur recursions are also given from the pyramidal point of view. They turn out to be useful in this form for the implementation of generating and whitening filters.