  We study the problem of parameter estimation for discretely observed
stochastic processes driven by additive small L\'{e}vy noises. We do not impose
any moment condition on the driving L\'{e}vy process. Under certain regularity
conditions on the drift function, we obtain consistency and rate of convergence
of the least squares estimator (LSE) of the drift parameter when a small
dispersion coefficient $\varepsilon \to 0$ and $n \to \infty$ simultaneously.
The asymptotic distribution of the LSE in our general setting is shown to be
the convolution of a normal distribution and a distribution related to the jump
part of the L\'evy process.
