Parametrical statistical and analytical modeling of distributions in nonlinear stochastic systems on manifolds

Discrete parametrical statistical and analytical modeling methods in nonlinear Ito stochastic systems on manifolds with Wiener and Poisson noises have been developed. For one- and multidimensional densities parametrization, the coefficients in orthogonal expansions of different orders are taken. Special attention is paid to nonlinear correlational theory of statistical and analytical modeling.