A Wold-Like Decomposition of Two-Dimensional Discrete Homogeneous Random Fields

摘要: Imposing a total order on regular two-dimensional discrete random field induces an orthogonal decomposition of the into two components: purely indeterministic and deterministic field. The component is further orthogonally decomposed half-plane countable number mutually evanescent fields. Each fields generated by column-to-column innovations with respect to different nonsymmetrical-half-plane total-ordering definition. has no innovations, nor any This results in corresponding spectral measure sum singular measures.