Estimation of all parameters in the fractional Ornstein-Uhlenbeck model under discrete observations

Let the Ornstein-Uhlenbeck process (X-t)(t >= 0) driven by a fractional Brownian motion BH described by dX(t) = -theta X(t)dt + sigma dB(t)(H) be observed at discrete time instants t(k) = kh, k = 0, 1, 2, ..., 2n+2. We propose an ergodic type statistical estimator (theta) over cap (n), (H) over cap (n) and (sigma) over cap (n) to estimate all the parameters theta, H and sigma in the above Ornstein-Uhlenbeck model simultaneously. We prove the strong consistence and the rate of convergence of the estimator. The step size h can be arbitrarily fixed and will not be forced to go zero, which is usually a reality. The tools to use are the generalized moment approach (via ergodic theorem) and the Malliavin calculus.