NONCENTRAL CONVERGENCE OF MULTIPLE INTEGRALS

• 成果类型: Article
• 署名作者: Nourdin, Ivan; Peccati, Giovanni
• 署名单位: Universite Paris Cite; Sorbonne Universite; Universite Paris Nanterre; Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP435
• 发表日期: 2009
• 页码: 1412-1426
• 关键词: CENTRAL LIMIT-THEOREMS; nonlinear functionals

摘要

Fix nu > 0, denote by G(nu/2) a Gamma random variable with parameter nu/2 and let n >= 2 be a fixed even integer. Consider a sequence {F-k}(k >= 1) of square integrable random variables belonging to the nth Wiener chaos of a given Gaussian process and with valiance converging to 2 nu. As k -> infinity, we prove that F-k converges in distribution to 2G(nu/2) - nu if and only if E(F-k(4)) - 12E(F-k(3)) -> 12 nu(2) - 48 nu.