Parameter Estimation for Ornstein-Uhlenbeck Driven by Ornstein-Uhlenbeck Processes with Small Levy Noises

In this paper, we consider the problem of parameter estimation for Ornstein-Uhlenbeck driven by Ornstein-Uhlenbeck processes with small Levy noises, based on discrete observations at n regularly spaced time points t(i) = i/n, i = 1, 2, ..., n, on [0, 1]. Under certain conditions, we obtain the consistency and the rate of convergence of the least squares estimator when a small dispersion parameter epsilon tends to 0 and n -> infinity simultaneously. Additionally, the asymptotic distribution of the estimator is established.