Parameter estimation for fractional Ornstein-Uhlenbeck processes

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We study a least squares estimator θₜ for the Ornstein-Uhlenbeck process, dXₜ=θXₜ dt+σdBʰₜ, driven by fractional Brownian motion Bʰ with Hurst parameter H≥ 12. We prove the strong consistence of θₜ (the almost surely convergence of θₜ to the true parameter % θ). 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 θₜ defined by (4.1).