Probability functional of a vector non-Gaussian Markov process and its communication application

A vector process with an arbitrary probability density function is presented as the solution of a system of nonlinear stochastic differential equations. Such a generative approach provides an opportunity to describe the process explicitly with the help of its probability functional without having to solve the corresponding vector Fokker–Planck equation. Direct synthesis of an optimal signals’ detection algorithm for communication channels with additive non-Gaussian correlated interference as an example of the probability functional application is considered.