Analytical modeling of distributions in stochastic systems on manifolds based on ellipsoidal approximation

Accuracy and sensitivity problems for algorithms of structural analytical modeling of one- and multidimensional distributions based on the method of ellipsoidal approximation (MEA) and the method of ellipsoidal linearization (MEL) are considered. General algorithms of ellipsoidal stochastic analysis in nonlinear stochastic systems on manifolds (MStS) with Wiener and Poisson noises are developed. Special attention is paid to MStS with additive noises. Accuracy and sensitivity equations are presented. For two-dimensional nonlinear circular MStS, accuracy and sensitivity equations are derived. Equations make it possible to calculate probability moments up to the fourth order. Algorithms based on orthogonal expansion of one-dimensional density are compared with algorithms based on MEA (MEL). Some generalizations are given.