Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process

Abstract

We study the minimum Skorohod distance estimation θ ε ∗ and minimum L 1 -norm estimation θ ε ˜ of the drift parameter θ of a stochastic differential equation d X t = θ X t d t + ε d L t d , X 0 = x 0 , where { L t d , 0 ≤ t ≤ T } is a fractional Lévy process, ε ∈ ( 0 , 1 ] . We obtain their consistency and limit distribution for fixed T, when ε → 0 . Moreover, we also study the asymptotic laws of their limit distributions for T → ∞ .