Analytical modeling of normal processes in stochastic systems with integral nonlinearities (III)

Methodological and algorithmical support for analytical modeling of normal (Gaussian) processes in differential stochastic systems with probabilistic integral nonlinearities (IN) based on Pearson distributions (PD) and stable probabilistic distributions (SPD) is presented. Support is based on the methods of statistical linearization (MSL) and normal approximation (MNA). Probabilistic IN were approximated by power expansions. The MSL and MNA coefficients for probabilistic IN based on PD and SPD are given. The MSL coefficients for incomplete beta-function and $F$-distribution are considered. Some SPD types are described. Test examples with accuracy estimation are given. Results may be generalized as new types of probabilistic IN (multichannel angular, spherical, etc.) and various numerical approximations (polynomial, rational, fractional rational, orthogonal, asymptotic, and iterative).