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Parameter estimation for fractional Ornstein–Uhlenbeck processes

Parameter estimation for fractional Ornstein–Uhlenbeck processes,10.1016/j.spl.2010.02.018,Statistics & Probability Letters,Yaozhong Huand,David Nuala

Parameter estimation for fractional Ornstein–Uhlenbeck processes   (Citations: 6)
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We study a least squares estimator θ̂T for the Ornstein–Uhlenbeck process, dXt=θXtdt+σdBtH, driven by fractional Brownian motion BH with Hurst parameter H≥12. We prove the strong consistence of θ̂T (the almost surely convergence of θ̂T to the true parameter θ). We also obtain the rate of this convergence when 1/2≤H3/4, 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.
Journal: Statistics & Probability Letters - STAT PROBAB LETT , vol. 80, no. 11, pp. 1030-1038, 2010
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