Theory of Control Stochastic Systems with Unsolved Derivatives

Various types of stochastic differential systems with unsolved derivatives (SDS USD) arise in problems of analytical modeling and estimation (filtering, extrapolation, etc.) for control stochastic systems, when it is possible to neglect higher-order time derivatives. Methodological and algorithmic support of analytical modeling, filtering, and extrapolation for SDS USD is developed. The methodology is based on the reduction of SDS USD to SDS by means of linear and nonlinear regression models. Two examples that are illustrating stochastic aspects of methodology are presented. Special attention is paid to SDS USD with multiplicative (parametric) noises.