We study multi-dimensional normal approximations on the Poisson space by means of Malliavin calculus, Stein's method and probabilistic interpolations. Our results yield new multi-dimensional central limit theorems for multiple integrals with respect to Poisson measures - thus significantly extending previous works by Peccati, Solé, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein-Uhlenbeck Lévy processes) are discussed in detail.
"Multi-Dimensional Gaussian Fluctuations on the Poisson Space." Electron. J. Probab. 15 1487 - 1527, 2010. https://doi.org/10.1214/EJP.v15-813