Approximation of the Numerical Simulation in Conjunction with One Data Assimilation Method by Stochastic Process of Ornstein-Uhlenbeck Type

The convergence of the results of modeling with the assimilation of observational data to a random process is considered. The assimilation of observational data is realized by the previously derived author's method. The convergence is considered when time of simulation is increasing unlimited. The conditions of convergence to the Ornstein-Uhlenbeck process are formulated and the corresponding results are proved. The physical interpretation of these conditions are discussed A possible numerical experiment to test and to apply these method is proposed and performed.