Berry-Esseen bounds for the least squares estimator for discretely observed fractional Ornstein-Uhlenbeck processes

Let theta > 0. We consider a one-dimensional fractional Ornstein-Uhlenbeck process defined as dX(t) = -theta X(t)dt + dB(t), t >= 0, where B is a fractional Brownian motion of Hurst parameter H is an element of (1/2, 1). we are interested in the problem of estimating the unknown parameter theta. For that purpose, we dispose of a discretized trajectory, observed at n equidistant times t(i) = i Delta(n), i = 0, ... , n, and T-n = n Delta(n) denotes the length of the 'observation window'. We assume that Delta(n) -> 0 and T-n -> infinity as n -> infinity. As an estimator of theta we choose the least squares estimator (LSE)(theta) over cap (n). The consistency of this estimator is established. Explicit bounds for the Kolmogorov distance, in the case when H is an element of (1/2, 3/4), in the central limit theorem for the LSE (theta) over cap (n) are obtained. These results hold without any kind of ergodicity on the process X. (C) 2013 Elsevier B.V. All rights reserved.