Parameter estimation for fractional Ornstein-Uhlenbeck processes
نویسنده
چکیده
We study a least squares estimator b θT for the Ornstein-Uhlenbeck process, dXt = θXtdt+σdB H t , driven by fractional Brownian motion B H with Hurst parameter H ≥ 1 2 . We prove the strong consistence of b θT (the almost surely convergence of b 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 θ̃T defined by (4.1).
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