Multi-dimensional Gaussian fluctuations on the Poisson space

被引：0

作者：

Peccati, Giovanni ^{[1
]}

Zheng, Cengbo ^{[2
,3
]}

机构：

[1] UR Math, Fac Sci Technol & Commun, L-1359 Luxembourg, Luxembourg

[2] Univ Paris 06, LPMA, Paris, France

[3] Univ Paris Ouest Nanterre Defense, Equipe ModalX, F-92000 Nanterre, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2010年 / 15卷

关键词：

Central Limit Theorems; Malliavin calculus; Multi-dimensional normal approximations; Ornstein-Uhlenbeck processes; Poisson measures; Probabilistic Interpolations; Stein's method; CENTRAL LIMIT-THEOREMS; MULTIVARIATE NORMAL APPROXIMATION; STEINS METHOD;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 multidimensional central limit theorems for multiple integrals with respect to Poisson measures - thus significantly extending previous works by Peccati, Sole, Taqqu and Utzet. Several explicit examples (including in particular vectors of linear and non-linear functionals of Ornstein-Uhlenbeck Levy processes) are discussed in detail.

引用

页码：1487 / 1527

页数：41

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