Minimum distance parameter estimation for Ornstein–Uhlenbeck processes driven by Lévy process

We consider the minimum Skorohod distance estimate θε∗ of the parameter θθ of a stochastic differential equation dXt=θXtdt+εdZt, X0=x0X0=x0 where {Zt,0≤t≤T}{Zt,0≤t≤T} is a centered Lévy process, ε∈(0,1]ε∈(0,1]. Its consistency and its limit distribution are studied for fixed TT, when ε→0ε→0. Furthermore, the asymptotic law of its limit distribution is studied for T→∞T→∞.