Least squares estimator for discretely observed Ornstein–Uhlenbeck processes with small Lévy noises

We study the problem of parameter estimation for generalized Ornstein–Uhlenbeck processes with small Lévy noises, observed at n regularly spaced time points on 0, 1]. Least squares method is used to obtain an estimator of the drift parameter. The consistency and the rate of convergence of the least squares estimator (LSE) are established when a small dispersion parameter ε→0 and n→∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a stable distribution. The obtained results are different from the classical cases where asymptotic distributions are normal.