Probability functional of a vector non-Gaussian Markov process

A large number of investigations have been carried out on the sufficient statistical characterization of different origins of interference. In some communication, radar and acoustic applications the Gaussian noise model is often not appropriate. For synthesis of an optimal signal detection algorithm we need an adequate statistical description of the interference, but the probability density function (PDF) of any limited dimension only specifies a certain equivalence class of random processes. Their sample paths may be quite different, so such a finite description cannot be considered to be an exhaustive approach. In this regard, it would be very attractive to describe a process by a single "continuous probability density", or a probability functional. In this paper we consider the explicit statistical description of a continuous vector Markov process in the form of its probability functional. Such a process is represented as a solution of a certain system of stochastic differential equations with parameters depending on the probability density function and correlation interval of the process components. Such a generative approach is very attractive as a tool for simulating real noise as it gives the opportunity to describe analytically a correlated non-Gaussian process and since it provides synthesis of optimal signal detection algorithms in the corresponding interference environment.