Asymptotic expansion of the drift estimator for the fractional Ornstein-Uhlenbeck process

We present an asymptotic expansion formula of an estimator for the drift coefficient of the fractional Ornstein-Uhlenbeck process. As the machinery, we apply the general expansion scheme for Wiener functionals recently developed by the authors [26]. The central limit theorem in the principal part of the expansion has the classical scaling T1/2. However, the asymptotic expansion formula is a complex in that the order of the correction term becomes the classical T-1/2 for H in (1/2,5/8), but T4H-3 for H in [5/8, 3/4).