Central Limit Theorems on Wiener space: diagram formulae, stochastic time-changes and quadratic functionals

We present necessary and sufficient conditions, to have that a sequence of multiple stochastic Wiener-Itô integrals converge in law towards a standard Gaussian random variable. These results are obtained through a classic result of stochastic calculus, known as the Dambis-Dubins-Schwarz theorem, stating that every Brownian martingale can be represented as a time-changed Brownian motion. Relations with the classic "method of moments" (via diagram formulae) will be discussed, as well as some motivations from the study of quadratic functionals of Gaussian processes. The content of the talk is related to some joint papers with D. Nualart (University of Barcelona) and C. Tudor (University of Paris I)