Least squares estimators for stochastic differential equations driven by small Lévy noises

•We consider parameter estimation for stochastic processes driven by Lévy noises.•We propose least squares estimator for the drift parameters.•Consistency and rate of convergence of the estimator are established.•A simulation study illustrates the asymptotic behavior of the estimator.

We study parameter estimation for discretely observed stochastic differential equations driven by small Lévy noises. We do not impose Lipschitz condition on the dispersion coefficient function σ and any moment condition on the driving Lévy process, which greatly enhances the applicability of our results to many practical models. Under certain regularity conditions on the drift and dispersion functions, we obtain consistency and rate of convergence of the least squares estimator (LSE) of parameter when ε→0 and n→∞ simultaneously. We present some simulation study on a two-factor financial model driven by stable noises.