Minimum distance parameter estimation for Ornstein-Uhlenbeck processes driven by Levy process

We consider the minimum Skorohod distance estimate theta(epsilon)* of the parameter theta of a stochastic differential equation dX(t) = theta X-t dt + epsilon dZ(t), X-0 = x(0) where {Z(t), 0 <= t <= T} is a centered Levy process, epsilon is an element of (0, 1]. Its consistency and its limit distribution are studied for fixed T, when epsilon -> 0. Furthermore, the asymptotic law of its limit distribution is studied for T -> infinity. (C) 2009 Elsevier B.V. All rights reserved.