On parameter estimation of the hidden Ornstein–Uhlenbeck process

Abstract

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.