Least squares estimator for Ornstein–Uhlenbeck processes driven by small fractional Lévy noises

Abstract

In this paper, we study the problem of parameter estimation for the Ornstein–Uhlenbeck processes{dXt=θXtdt+dYt dYt=Ytdt+εdLtd driven by Ornstein–Uhlenbeck processes with small fractional Lévy noises and Yt can be observed, based on discrete high frequency observations at regularly spaced time points {tk=kn, k=1, …, n} on [0, 1]. We obtain the consistency as well as the asymptotic behavior of the least squares estimator of the unknown parameter θ when ε→0 and n→∞ simultaneously.