Applications of orthogonal expansions for analytical modeling of multidimensional distributions in stochastic systems on manifold

Problems of accuracy and sensitivity estimation for algorithms of the analytical modeling method (AMM) based on the multidimensional orthogonal expansions method (OEM) and quasi-moments (QMM) in stochastic systems on manifolds (MStS) with Wiener and Poisson noises are considered. Equations for multidimensional OEM and QMM are given. Problems of reduction of the number of equations for OEM and QMM are discussed. For typical reliability and security problems, equations for OEM and QMM sensitivity functions of the first order are deduced. The results are the basis of the symbolic software tools in MATLAB-MAPLE. A test example for scalar stochastic systems with cybic nonlinearity and multiplicative Gaussian noise is given. Some generalizations are presented.