Moments methods for analytical modeling of stochastic systems on manifolds

Problems of accuracy and sensitivity estimation for algorithms of analytical modeling methods (AMM) based on one- and multidimensional initial moments methods (IMM) and central moments method (CMM) in stochastic systems on manifolds (MStS) with Wiener and Poisson noises are considered. For typical reliability and security problems accuracy and sensitivity, equations for AMM are given. Problems of reduction of equations for IMM and CMM are discussed. The results are the basis of symbolic software tools in MATLAB-MAPLE. A test example for scalar MStS with cubic nonlinearity and multiplicative Gaussian noise is given. Some generalizations are presented.