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 nn regularly spaced time points ti=i/n,i=1,…,n 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→0ε→0 and n→∞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.