Parameter estimation for Ornstein-Uhlenbeck processes driven by α-stable Lévy motions

The parameter estimation theory for stochastic dieren tial equa- tions driven by Brownian motions or general L evy processes with nite second moments has been well developed. In this paper, we consider the parameter estimation problem for Ornstein-Uhlenbeck processes driven by -stable L evy motions. The classical maximum likelihood method does not apply in this context because the likelihood ratio does not exist. We shall use the trajec- tory tting method combined with the weighted least squares technique. We discuss the consistency and the asymptotic distributions of our estimators for general weights in both the ergodic and the non-ergodic cases.