Geodesic
On the prediction of a class of random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 175-182 
L. I. Piterbarg. On the prediction of a class of random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 28 (1983) no. 1, pp. 175-182. http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a14/
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     author = {L. I. Piterbarg},
     title = {On the prediction of a~class of random fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {175--182},
     year = {1983},
     volume = {28},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1983_28_1_a14/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.