Models of discontinous random fields

When the theory of state variables is applied to optimal synthesis of signal processing devices in space-time channels, it becomes necessary to simulate signals and interference with stochastic partial differential equations. Models of interference are discontinuous random fields, typically with a Poisson distribution. Stochastic partial differential equations generating such fields as their solution include a linear equation, wave equations such as those describing propagation through randomly nonhomogeneous media, and Kollmogorov-Feller equations corresponding to point or multipoint probability distributions. The statistical characteristics of stationary uniform fields satisfying these equations are analyzed, assuming that such discontinuous random fields exist.