2-D-Recursive Modelling of Homogeneous Discrete Gaussian Markov Fields

A 2-D-stochastic realization is obtained for an homogeneous discrete Gaussian Markov-field in two dimensions. In specific, it is shown that such Markov fields can be represented as the (unique) pathwise solution of a 2-D-recursive system of equations, with a locally-correlated “forcing-noise.” The idea of stochastic “dynamic” system in two dimensions gets realized this way. Two types of domain are considered: spheric and rectangular.