Joint filtration and recognition of normal proсesses in stochastic systems with unsolved derivatives

Methodological and algorithmic support for analytical modeling, estimation, identification, and calibration for essentially nonstationary (e. g., shock) stochastic systems with unsolved derivatives (StS USD) is worked out. It is supposed that state equations contain observation vector. After survey, classes of regression equations for StS USD are considered. Basic results: ($i$) for general StS USD, optimal algorithms of joint filtration and recognition are presented; ($ii$) for linear Gaussian equations, optimal algorithms of joint linear filtration and recognition are given; ($iii$) for StS USD, linear relatively on $X_t$ and nonlinear relatively on $Y_t$ algorithm is described; and ($i\nu$) in case of result ($iii$), using the method of normal approximation, the corresponding algorithm is developed. A scalar example of nonlinear StS USD with Gaussian noise corresponding algorithm is given and discussed. Some potential generalizations are presented.