Hidden Ergodic Ornstein-Uhlenbeck Process and Adaptive Filter

The model of partially observed linear stochastic differential equations depending on some unknown parameters is considered. An proximation of the unobserved component is proposed. This approximation is realized in three steps. First an estimator of the thod of moments of unknown parameter is constructed. Then this estimator is used for defining the One-step MLE-process and nally the last estimator is substituted to the equations of Kalman-Bucy (K-B) filter. The solution of obtained K-B equations ovide us the approximation (adaptive K-B filter). The asymptotic properties of all mentioned estimators and MLE and Bayesian timators of the unknown parameters are described. The asymptotic efficiency of the proposed adaptive filter is shown.