Central limit theorems for sequences of multiple stochastic integrals

• 成果类型: Article
• 署名作者: Nualart, D; Peccati, G
• 署名单位: University of Barcelona; Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000621
• 发表日期: 2005
• 页码: 177-193
• 关键词: wiener; functionals; expansions

摘要

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting behavior of quadratic functionals of Gaussian processes.