Parameter estimation for Ornstein–Uhlenbeck processes of the second kind driven by α-stable Lévy motions

Abstract

ABSTRACTIn this article, we study the problem of parameter estimation for Ornstein–Uhlenbeck processes of the second kind driven by α-stable Lévy motions, based on continuous and discrete observations, respectively. Using the trajectory fitting method combined with the weighted least-squares technique, we discuss the consistency and the asymptotic distributions of the estimators for general weights in both the ergodic and the non ergodic cases.