Analytical Synthesis of the Probabilistic Characteristics of One Class of Non-Markovian Processes

Abstract

Nowadays analytical methods for synthesis of probabilistic characteristics of random processes exist only for Markovian processes and are based on solution of the Fokker-Plank-Kolmogorov equation. The article presents an approach that allows us to solve such a problem for non-Markovian processes, which are described by approximated solutions of stochastic nonlinear integrated equations in general form. The basis for the method proposed is a representation of the integral equation by two-point boundary-value problem with its subsequent solution by the invariant embedding method.