  We consider the problem of the simulation of Levy-driven stochastic
differential equations. It is generally impossible to simulate the increments
of a Levy-process. Thus in addition to an Euler scheme, we have to simulate
approximately these increments. We use a method in which the large jumps are
simulated exactly, while the small jumps are approximated by Gaussian
variables. Using some recent results of Rio about the central limit theorem, in
the spirit of the famous paper by Komlos-Major-Tsunady, we derive an estimate
for the strong error of this numerical scheme. This error remains reasonnable
when the Levy measure is very singular near 0, which is not the case when
neglecting the small jumps.
  In the same spirit, we study the problem of the approximation of a
Levy-driven S.D.E. by a Brownian S.D.E. when the Levy process has no large
jumps.
