The precise asymptotic behavior of parameter estimators in Ornstein–Uhlenbeck process

In the present paper, we study the asymptotic behavior for estimator of the drift parameter in an Ornstein–Uhlenbeck process. The L r -convergence rate and the precise asymptotics in the law of iterated logarithm and in the law of logarithm for the estimator are obtained. Moreover, we also get the complete moment convergence of this estimator. The main method of this paper is the deviation inequality for the quadratic functional.