On the prediction of a class of random fields

We consider a class of random fields which is a generalization of a class of homogeneous random fields with rational spectral density. This class contains Gaussian Markov fields. In the Gaussian case the splitting $\sigma$-algebras for a bounded region with smooth boundary are described. We deduce also an explicit linear prediction formula (based on the observations in the bounded region) for a homogeneous isotropic field with rational spectral density.