Central limit theorems for sequences of multiple stochastic integrals

This is the published version, also available here: http://dx.doi.org/10.1214/009117904000000621.We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes