Evaluation of the One-Dimensional Probability Densities and Moments of a Random Process in the Output of an Essentially Non-Linear System

This paper considers non-linear systems with feed-back. These systems contain non-linear functional transforms, which are separated by linear filters with rational spectra.
In order to evaluate the single-dimensional probability density and the moments of a random process in the output of the system, a multi-dimensional random Markov process is constructed, and the Kolmogorov diffusion equations are employed.
The exact results obtained by using this method are compared with the results of an approximate “statistical linearization” approach for one system. The two sets of results are found to agree well.