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.
"Central limit theorems for sequences of multiple stochastic integrals." Ann. Probab. 33 (1) 177 - 193, January 2005. https://doi.org/10.1214/009117904000000621