Stein's method on Wiener chaos
Stein's method on Wiener chaos
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DOI：
10.1007/s00440-008-0162-x
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发表时间：
2009-09-01
影响因子：
2
通讯作者：
Peccati, Giovanni
中科院分区：
文献类型：
--
作者：
Nourdin, Ivan;Peccati, Giovanni
将Malliavin演算与Stein方法相结合，得到了一般高斯过程的固定Wiener混沌中随机变量的Gauss型和Gamma型逼近的显式界。我们的方法推广、细化和统一了Nourdin、Nualart、Ortiz-Latorre、Peccati和Tudor最近证明的多重Wiener-it积分的中心和非中心极限定理。我们利用我们的技巧证明了分数次布朗运动的从属泛函的Breuer-重大CLT中的Berry-Esseen界。利用著名的Ornstein-Uhlenbeck半群的Mehler公式，我们还恢复了Chatterjee最近证明的关于有限维高斯向量泛函的高斯逼近的一个技术结果。
We combine Malliavin calculus with Stein's method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-It integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nualart, Ortiz-Latorre, Peccati and Tudor. We apply our techniques to prove Berry-Esseen bounds in the Breuer-Major CLT for subordinated functionals of fractional Brownian motion. By using the well-known Mehler's formula for Ornstein-Uhlenbeck semi-groups, we also recover a technical result recently proved by Chatterjee, concerning the Gaussian approximation of functionals of finite-dimensional Gaussian vectors.