Analytical modeling of normal processes in stochastic systems with complex nonlinearities

Differential stochastic systems (DStS) with Wiener and Poisson noises and complex finite, differential, and integral nonlinearities and hereditary StS reducible to DStS are considered. Equations and algorithms of analytical modeling based on the normal approximation method (NAM) and the statistical linearization method (SLM) are given. The case of complex continuous and discontinuous nonlinearities of scalar and vector arguments is considered. Special attention is paid to NAM (SLM) typical integrals for finite rational and irrational nonlinear and integral scalar and vector nonlinear functions. The general case of integral nonlinearities reducible to linear is considered. Test examples are given.