QUANTITATIVE STABLE LIMIT THEOREMS ON THE WIENER SPACE

• 成果类型: Article
• 署名作者: Nourdin, Ivan; Nualart, David; Peccati, Giovanni
• 署名单位: Universite de Lorraine; University of Luxembourg; University of Kansas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP965
• 发表日期: 2016
• 页码: 1-41
• 关键词: fractional brownian-motion; multiple stochastic integrals; weighted quadratic variations; malliavin calculus; asymptotic-behavior; gaussian-processes; power variations; steins method; CONVERGENCE; Respect

摘要

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize previous works by Nourdin and Nualart [J. Theoret. Probab. 23 (2010) 39-64] and Harnett and Nualart [Stochastic Process. Appl. 122 (2012) 3460-3505], and provide a substantial contribution to a recent line of research, focussing on limit theorems on the Wiener space, obtained by means of the Malliavin calculus of variations. Applications are given to quadratic functionals and weighted quadratic variations of a fractional Brownian motion.