2D-recursive stochastic realization of discrete Gaussian Markov fields: the homogeneous case on a spheric domain

A 2D-stochastic realization is obtained for an homogeneous discrete Gaussian Markov-field in two dimensions. In specific, it is shown that the Markov field at issue can be represented as the (unique) pathwise solution of a stochastic system in two dimension, whose input is a locally-correlated `forcing-noise'. The result is obtained for Markov-fields `living' on a spheric domain, which allows to simplify the treatment of the subject, nevertheless being not really restrictive with respect to the more `natural' case of a rectangular domain.