Normal Approximation on a Finite Wiener Chaos

DOI10.1007/978-3-319-11292-3_14zbMath1391.60071OpenAlexW127246669MaRDI QIDQ5374168

David Nualart

Publication date: 9 April 2018

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-11292-3_14

zbMATH Keywords

Malliavin calculusStein's methodWiener chaostotal variation distance

Mathematics Subject Classification ID

Gaussian processes (60G15) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Enumeration in graph theory (05C30) Stochastic calculus of variations and the Malliavin calculus (60H07) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

Uses Software

• longmemo

Cites Work

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• Fisher information and the fourth moment theorem
• Absolute continuity and convergence of densities for random vectors on Wiener chaos
• The determinant of the iterated Malliavin matrix and the density of a pair of multiple integrals
• Quantitative Breuer-Major theorems
• Riesz transform and integration by parts formulas for random variables
• Central limit theorems and quadratic variations in terms of spectral density
• Stein's method on Wiener chaos
• Density convergence in the Breuer-Major theorem for Gaussian stationary sequences
• Stein's method and exact Berry-Esseen asymptotics for functionals of Gaussian fields
• Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
• Central limit theorems for non-linear functionals of Gaussian fields
• Renormalized self-intersection local time for fractional Brownian motion
• Convergence in total variation on Wiener chaos
• Entropy and the fourth moment phenomenon
• Convergence of densities of some functionals of Gaussian processes
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• Central limit theorems for sequences of multiple stochastic integrals
• The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals
• Normal Approximations with Malliavin Calculus
• The Malliavin Calculus and Related Topics
• Distributional and \(L^q\) norm inequalities for polynomials over convex bodies in \(\mathbb{R}^n\)