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Normal Approximation on a Finite Wiener Chaos

  • David NualartEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 100)

Abstract

The purpose of this note is to survey some recent developments in the applications of Malliavin calculus combined with Stein’s method to derive central limit theorems for random variables on a finite sum of Wiener chaos. Starting from the fourth moment theorem by Nualart and Peccati [23], we will discuss several related topics such as conditions for the convergence in total variation, absolute continuity of probability laws and uniform convergence of densities under suitable non degeneracy assumptions. The fact that the random variables belong to a fixed Wiener chaos (or to a finite sum of Wiener chaos) will play a fundamental role in the results.

Keywords

Malliavin calculus Wiener chaos Total variation distance Stein’s method 

2010 Mathematics Subject Classification

60G15 60H07 60H10 65C30 

Notes

Acknowledgments

We would like to thank an anonymous referee for carefully reading this manuscript and providing useful remarks.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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