Analytical modeling of stochastic systems with random parameters and unsolved derivatives

The paper is devoted to nonlinear correlation methods for analytical modeling in differential stochastic systems with unsolved derivatives (StS USD) and random parameters. Survey is given. Necessary notations concerning integral canonical expansions (ICE) and its linear and nonlinear transforms are presented. It is shown how differential StS USD can be reduced to differential StS. Basic quality analysis algorithms for reducible StS USD are described. Special attention is paid to multicomponent ICE theory of stochastic processes and StS USD reducible to the differential ones. Two types of nonlinear transforms based on linear ICE regression are developed. Normal approximation method is used for ordinary differential equations for conditional probabilistic characteristics: mathematical expectations, covariance matrix, and matrix of covariance functions. For uncondional characteristics, ICE method is implemented. Analytical modeling methods are presented both for stationary and nonstationary regimes. An illustrative example is given. Directions of future generalizations are given.