Stochastic versus dynamic approach to Lévy statistics in the presence of an external perturbation

We study the influence of a dissipation process on diffusion dynamics triggered by slow fluctuations. We study both strong- and weak-friction regimes. When the latter regime applies, the system is attracted by the basin of either Gauss or Lévy statistics according to whether the fluctuation correlation function is integrable or not. We analyze with a numerical calculation the border between the two basins of attraction