Parameter estimation for fractional Ornstein-Uhlenbeck processes

We study a least squares estimator for the Ornstein-Uhlenbeck process, , driven by fractional Brownian motion BH with Hurst parameter . We prove the strong consistence of (the almost surely convergence of to the true parameter [theta]). We also obtain the rate of this convergence when 1/2<=H<3/4, applying a central limit theorem for multiple Wiener integrals. This least squares estimator can be used to study other more simulation friendly estimators such as the estimator obtained by a function of .