Rates of convergence of approximate maximum likelihood estimators in the Ornstein-Uhlenbeck process ☆

Berry-Esseen bounds, with random and nonrandom normings, and large deviation probability bounds for two approximate maximum likelihood estimators of the drift parameter in the Ornstein-Uhlenbeck process are obtained when the process is observed at equally spaced dense time points. Also obtained are the rates at which these estimators converge to the maximum likelihood estimator based on continuous observation.