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Multi-Dimensional Gaussian Fluctuations on the Poisson Space

   
@article{EJP813,
	author = {Peccati Giovanni and Cengbo Zheng},
	title = {Multi-Dimensional Gaussian Fluctuations on the Poisson Space},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {Central Limit Theorems; Malliavin calculus; Multi-dimensional normal approximations; Ornstein-Uhlenbeck processes; Poisson measures; Probabilistic Interpolations; Stein's method},
	abstract = {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.},
	pages = {no. 48, 1487-1527},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-813},    
        url = {http://ejp.ejpecp.org/article/view/813}}