On identification of linear dynamic systems with an unknown distribution of the noises

The problem of construction of the probabilistic models for dynamic systems with unknown noise distribution is considered. The proposed approach is based on the construction of one-step predictors and estimators for the limiting probability density for the sequence of forecast errors. The estimates for this probability density and its derivatives with improved convergence rate in mean square sense are given and studied. This forecasting method is applied to linear dynamic systems. In this case the presence of the dependence in the sequence of forecast errors doesn´t influence asymptotical properties of estimates of the probability density and its derivatives. The convergence with probability 1 and uniform asymptotic normality of estimates are proved. The estimation problems of the limiting probability density have been solved also in the case of the martingale difference noise both for the deterministic and stochastic regression processes