2D-Recursive Stochastic Realization of Discrete Gaussian Markov Fields: the Homogeneous Case on a Spheric Domain

A 2D-stocastic realization is obtained for an ho- mogeneous 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.