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Parameter estimation for fractional Ornstein-Uhlenbeck processes. (English) Zbl 1187.62137
Summary: We study a least squares estimator θ ^ T for the Ornstein-Uhlenbeck process, dX t =θX t dt+σdB t H , driven by fractional Brownian motion B H with Hurst parameter H1/2. We prove the strong consistence of θ ^ T (the almost surely convergence of θ ^ T to the true parameter θ). We also obtain the rate of this convergence when 1/2H<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 θ ˜ T obtained by a function of 0 T X t 2 dt.
MSC:
62M05Markov processes: estimation
62F12Asymptotic properties of parametric estimators
60F05Central limit and other weak theorems
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