Parameter estimation for fractional Ornstein–Uhlenbeck processes

We study a least squares estimator θ̂T for the Ornstein–Uhlenbeck process, dXt=θXtdt+σdBtH, driven by fractional Brownian motion BHBH with Hurst parameter H≥12. We prove the strong consistence of θ̂T (the almost surely convergence of θ̂T to the true parameter θθ). We also obtain the rate of this convergence when 1/2≤H<3/41/2≤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 θ̃T obtained by a function of ∫0TXt2dt.