Title: Parameter estimation for fractional Ornstein-Uhlenbeck processes of general Hurst parameter,
Abstract: This paper provides several statistical estimators for the drift and
volatility parameters of an Ornstein-Uhlenbeck process driven by fractional
Brownian motion, whose observations can be made either continuously or at
discrete time instants. First and higher order power variations are used to
estimate the volatility parameter. The almost sure convergence of the
estimators and the corresponding central limit theorems are obtained for all
the Hurst parameter range $H\in (0, 1)$. The least squares estimator is used
for the drift parameter. A central limit theorem is proved when the Hurst
parameter $H \in (0, 1/2)$ and a noncentral limit theorem is proved for
$H\in[3/4, 1)$. Thus, the open problem left in the paper by Hu and Nualart
(2010) is completely solved, where a central limit theorem for least squares
estimator is proved for $H\in [1/2, 3/4)$.