2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125322We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We extend our result to the multidimensional case and prove a weak convergence result for a sequence of square integrable random variables.16 pagesProbability60F05, 60G15text