STEIN'S METHOD AND NORMAL APPROXIMATION OF POISSON FUNCTIONALS

• 成果类型: Article
• 署名作者: Peccati, G.; Sole, J. L.; Taqqu, M. S.; Utzet, F.
• 署名单位: Universite Paris Saclay; Sorbonne Universite; Boston University; Autonomous University of Barcelona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP477
• 发表日期: 2010
• 页码: 443-478
• 关键词: CENTRAL LIMIT-THEOREMS; STOCHASTIC INTEGRALS; CONVERGENCE; asymptotics; PRINCIPLE; models

摘要

We combine Stein's method with a version of Malliavin calculus on the Poisson space. As a result, we obtain explicit Berry-Esseen bounds in Central limit theorems (CLTs) involving multiple Wiener-Ito integrals with respect to a general Poisson measure. We provide several applications to CLTs related to Ornstein-Uhlenbeck Levy processes.