On parameter estimation of hidden ergodic Ornstein-Uhlenbeck process

We consider the problem of parameter estimation for the partially observed linear stochastic differential equation. We assume that the unobserved Ornstein-Uhlenbeck process depends on some unknown parameter and estimate the unobserved process and the unknown parameter simultaneously. We construct the two-step MLE-process for the estimator of the parameter and describe its large sample asymptotic properties, including consistency and asymptotic normality. Using the Kalman-Bucy filtering equations we construct recurrent estimators of the state and the parameter.