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We study the problem of parameter estimation for discretely observedstochastic processes driven by additive small L\'{e}vy noises. We do not imposeany moment condition on the driving L\'{e}vy process. Under certain regularityconditions on the drift function, we obtain consistency and rate of convergenceof the least squares estimator (LSE) of the drift parameter when a smalldispersion coefficient $\varepsilon \to 0$ and $n \to \infty$ simultaneously.The asymptotic distribution of the LSE in our general setting is shown to bethe convolution of a normal distribution and a distribution related to the jumppart of the L\'evy process.

Least squares estimators for discretely observed stochastic processes driven by small Levy noises