Analytical modeling in stochastic systems on manifolds based on orthogonal expansions

Problems of accuracy and sensitivity of one-dimensional distributions by parametrical analytical modeling algorithms on the basis of the orthogonal expansion method (OEM) and the quasi-moment method (QMM) in stochastic systems on manifolds (MStS) are considered. Stochastic system on manifolds is described by Ito linear, linear with multiplicative noises and nonlinear equations with Wiener and Poisson noises. The OEM and QMM equations are derived by generalized Ito formula. Methodological results are the basis of the original symbolic software tools for MATLAB-MAPLE. The problems of reduction of number of OEM and QMM equations are discussed, reliability and security algorithms are presented. Scalar nonlinear MStS with multiplicative white noise is investigated. Some possible generalizations are formulated.