Analytical modeling of normal processes in stochastic systems with complex irrational nonlinearities

Stochastic systems (including manifolds) with Wiener and Poisson noises and complex irrational nonlinearities (CIRN) are considered. Equations and algorithms of analytical modeling based on the normal approximation method (NAM) and the statistical linearization method (SLM) are given. Typical integrals and software based on cylindrical functions for computing deterministic and stochastic CIRN are presented. Seven test examples for typical CIRN are given. Applications to Gibbs distributions and distributions with invariant measure are discussed.