Parametric analytical modeling of wide band processes in stochastic systems with unsolved derivatives

Methods of parametric analytical modeling (AMM) of stochastic processes in finite dimensional nonlinear stationary and nonstationary stochastic systems with unsolved derivatives are presented. Such models describe technical systems in control and informatics if one neglects transient processes. For analytical modeling and accuracy and sensitivity analysis, the author developed autocorrelated methods based on normal approximation and statistical linearization (NAM and SLM), orthogonal expansions (OEM), and other parametric methods for one- and multidimensional densities. Special attention is paid to AMM for discrete systems by OEM based on the Poisson distribution. Typical nonlinearities with unsolved derivatives and statistical linearization coefficients are given. Test examples are discussed. Algorithms are the basis of experimental software tools for safety and reliability analysis of technical systems that are being developed by the authors.