Moldavs'ka E. Methods of parameters identification in stohastic systems with weak and strong dependence dependence

The dissertation is devoted to investigation of parameters identification in stochastic systems with weak and strong dependence. Conditions of consistency and asymptotic normality are proposed for minimum contrast estimators of the spectral density of continuous time random fields in the stochastic systems with weak and strong dependence. Conditions of strong consistency of estimations obtained by minimization of the certain class functionals contained random processes with strong dependence are presented. It is proved that the least square estimation of parameters in the linear regression continuous time models with strong dependence and constraints on parameters normed with an appropriate matrix tends to the solution of the quadratic programming problem. This solution is a non-Gaussian random vector in the typical cases. The dissertation has a theoretical character. The results can also be applied in various areas of modern knowledge based on statistics of random processes and fields.