Stein’s method on Wiener chaos
نویسندگان
چکیده
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-Itô 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-Esséen bounds in the Breuer-Major CLT for subordinated functionals of fractional Brownian motion. By using the well-known Mehler’s formula for Ornstein-Uhlenbeck semigroups, we also recover a technical result recently proved by Chatterjee, concerning the Gaussian approximation of functionals of finitedimensional Gaussian vectors.
منابع مشابه
Stein’s method, Malliavin calculus, Dirichlet forms and the fourth moment theorem
The fourth moment theorem provides error bounds in the central limit theorem for elements of Wiener chaos of any order. It was proved by Nourdin and Peccati [31] using Stein’s method and the Malliavin calculus. It was also proved by Azmoodeh, Campese and Poly [3] using Stein’s method and Dirichlet forms. This paper is an exposition on the connections between Stein’s method and the Malliavin cal...
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