Fourth moment theorems on the Poisson space in any dimension

DOI10.1214/18-EJP168zbMath1387.60045arXiv1707.01889OpenAlexW2731183720MaRDI QIDQ1748942

Christian Döbler, Guangqu Zheng, Anna Vidotto

Publication date: 15 May 2018

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.01889

zbMATH Keywords

Stein's methodmultiple Wiener-Itô integralsGaussian approximationexchangeable pairs\textit{carré du champ} operatorfourth moment theoremsmultivariate Poisson functionalsPeccati-Tudor theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (11)

A Peccati-Tudor type theorem for Rademacher chaoses ⋮ Stein approximation for multidimensional Poisson random measures by third cumulant expansions ⋮ High-dimensional central limit theorems for homogeneous sums ⋮ A simplified second-order Gaussian Poincaré inequality in discrete setting with applications ⋮ Spherical Poisson waves ⋮ Unnamed Item ⋮ Fourth moment theorems on the Poisson space: analytic statements via product formulae ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ Stable limit theorems on the Poisson space ⋮ The multivariate functional de Jong CLT ⋮ New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Normal approximation of Poisson functionals in Kolmogorov distance
• Berry-Esseen bounds and multivariate limit theorems for functionals of Rademacher sequences
• Classical and free fourth moment theorems: universality and thresholds
• Multivariate Gaussian approximations on Markov chaoses
• Stein's method and the multivariate CLT for traces of powers on the compact classical groups
• The universality of homogeneous polynomial forms and critical limits
• Quantitative de Jong theorems in any dimension
• Normal approximation and almost sure central limit theorem for non-symmetric Rademacher functionals
• Nonnormal approximation by Stein's method of exchangeable pairs with application to the Curie-Weiss model
• On the Gaussian approximation of vector-valued multiple integrals
• Stein's method for dependent random variables occuring in statistical mechanics
• Multi-dimensional Gaussian fluctuations on the Poisson space
• Stein's method and stochastic analysis of Rademacher functionals
• Chaos of a Markov operator and the fourth moment condition
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• Stein's method on Wiener chaos
• Stein's method of exchangeable pairs for the Beta distribution and generalizations
• A note on the exchangeability condition in Stein's method
• Stein's method and normal approximation of Poisson functionals
• Multivariate normal approximation with Stein's method of exchangeable pairs under a general linearity condition
• The distribution of leading digits and uniform distribution mod 1
• On coupling constructions and rates in the CLT for dependent summands with applications to the antivoter model and weighted \(U\)-statistics
• The fourth moment theorem on the Poisson space
• On the fourth moment condition for Rademacher chaos
• Invariance principles for homogeneous sums: universality of Gaussian Wiener chaos
• Exchangeable pairs on Wiener chaos
• Semicircular limits on the free Poisson chaos: counterexamples to a transfer principle
• Discrete Malliavin-Stein method: Berry-Esseen bounds for random graphs and percolation
• Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws
• Universal Gaussian fluctuations on the discrete Poisson chaos
• Fourth moment theorems for Markov diffusion generators
• Central limit theorems for sequences of multiple stochastic integrals
• New Berry-Esseen bounds for non-linear functionals of Poisson random measures
• Normal Approximations with Malliavin Calculus
• On Stein’s method for multivariate normal approximation
• The Berry-Esseen bound for character ratios
• Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
• Stochastic Analysis for Poisson Processes

This page was built for publication: Fourth moment theorems on the Poisson space in any dimension