The multivariate functional de Jong CLT

• 成果类型: Article
• 署名作者: Doebler, Christian; Kasprzak, Mikolaj; Peccati, Giovanni
• 署名单位: Heinrich Heine University Dusseldorf; University of Luxembourg; Massachusetts Institute of Technology (MIT)
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01114-3
• 发表日期: 2022
• 页码: 367-399
• 关键词: universal gaussian fluctuations; LIMIT-THEOREMS; steins method; U-statistics; Invariance; approximations; moments; chaos; sums

摘要

We prove a multivariate functional version of de Jong's CLT (J Multivar Anal 34(2):275-289, 1990) yielding that, given a sequence of vectors of Hoeffdingdegenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in t = 1 vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the 'universality of Wiener chaos' phenomenon first observed in Nourdin et al. (Ann Probab 38(5):1947-1985, 2010).