Orthogonal decompositions of 2-D nonhomogeneous discrete random fields

Imposing a total-order on a 2-D discrete random eld induces an orthogonal decomposition of the random eld into two components: A purely-indeterministic eld and a deterministic one. The purely-indeterministic component is shown to have a 2-D whiteinnovations driven moving-average representation. The 2-D deterministic random eld can be perfectly predicted from the eld's \past" with respect to the imposed total order de nition. The deterministic eld is further orthogonally decomposed into an evanescent eld, and a remote past eld. The evanescent eld is generated by the column-to-column innovations of the deterministic eld with respect to the imposed non-symmetrical-half-plane total-ordering de nition. The presented decomposition can be obtained with respect to any non-symmetrical-half-plane total-ordering de nition, for which the non-symmetrical-halfplane boundary line has rational slope. Corresponding author:Telephone: +972-7-461842, email: [email protected]