  The aim of this paper is to establish a global asymptotic equivalence between
the experiments generated by the discrete (high frequency) or continuous
observation of a path of a L{\'e}vy process and a Gaussian white noise
experiment observed up to a time T, with T tending to $\infty$. These
approximations are given in the sense of the Le Cam distance, under some
smoothness conditions on the unknown L{\'e}vy density. All the asymptotic
equivalences are established by constructing explicit Markov kernels that can
be used to reproduce one experiment from the other.
