  We describe an Euler scheme to approximate solutions of L\'evy driven
Stochastic Differential Equations (SDE) where the grid points are random and
given by the arrival times of a Poisson process. This result extends a previous
work of the authors in Ferreiro-Castilla et al. (2012). We provide a complete
numerical analysis of the algorithm to approximate the terminal value of the
SDE and proof that the approximation converges in mean square error with rate
$\mathcal{O}(n^{-1/2})$. The only requirement of the methodology is to have
exact samples from the resolvent of the L\'evy process driving the SDE; classic
examples such as stable processes, subclasses of spectrally one sided L\'evy
processes and new families such as meromorphic L\'evy processes (cf. Kuznetsov
et al. (2011)) are some examples for which the implementation of our algorithm
is straightforward.
