Title: Small-time stable approximations of multidimensional Lévy processes

Abstract: We establish upper and lower bounds on the rate of convergence in the Wasserstein distance for wide classes of Lévy processes attracted to a multidimensional stable law in the small-time regime. We show that the rate of convergence is polynomial for the domain of normal attraction and slower than any polynomial for the domain of non-normal attraction. We will focus on the upper bounds, which are based on two couplings between arbitrary pure-jump Lévy processes.