The Mathematical Models of Transformation non-Gaussian Random Processes in the non-Linear non-Inertial Elements

Abstract

Issues related to creation of mathematical models and modeling of pre-formation of random processes, signals and noise in non-linear non-inertial elements were analyzed. The models were constructed and the non-Gaussian correlation processes were described in the form generated by the Gaussian noise. It is shown that the monotonic non-inneronic transformation does not change the order of the Markov process being transformed. The formation of stationary random processes specified by one-dimensional density of probability distribution and autocorrelation function is described. Values of coefficients determining autocorrelation function are obtained, at which the average quadratic deviation between the given and even correlation functions does not exceed a given value. Described is a mathematical transformation of random processes in non-linear non-inertial elements with one input and one output. A joint distribution of the output processes of a non-linear element with one input and several outputs, as well as with several inputs and outputs, is determined. Linear and quadratic transformation analysis was performed, in which the components of the output distribution are non-Gaussian. Analysis of the distribution density of linear functions of the same random process is carried out, at which the distribution density of the probability of the output process will repeat the probability distribution of the random process at the input.