2014/04/18 by Louis H. Y. Chen, Chen, Louis H. Y., Guillaume Poly +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR) #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1404.4784
openalex publication_date 2014/04/18 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
The fourth moment theorem provides error bounds of the order √\mathbb E(F4) - 3 in the central limit theorem for elements F of Wiener chaos of any order such that \mathbb E(F2) = 1. It was proved by Nourdin and Peccati (2009) using Stein's method and the Malliavin calculus. It was also proved by Azmoodeh, Campese and Poly (2014) using Stein's method and Dirichlet forms. This paper is an exposition on the connections between Stein's method and the Malliavin calculus and between Stein's method and Dirichlet forms, and on how these connections are exploited in proving the fourth moment theorem.