On parameter estimation of the hidden Ornstein-Uhlenbeck process

This paper considers parameter estimation in the Ornstein-Uhlenbeck process observed in the presence of Gaussian white noise. We show the consistency and asymptotic normality of the maximum likelihood estimator in small-noise asymptotics. The data are assumed to arise from a non-homogeneous partially observed linear system. The construction and study of the estimator are based mainly on the asymptotics of the equations of Kalman-Bucy filtration.