Fourth moment theorems on the Poisson space: analytic statements via product formulae

DOI10.1214/18-ECP196zbMath1406.60037arXiv1808.01836OpenAlexW2887509721MaRDI QIDQ1725482

Christian Döbler, Giovanni Peccati

Publication date: 14 February 2019

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

Full work available at URL: https://arxiv.org/abs/1808.01836

zbMATH Keywords

Malliavin calculusStein's methodBerry-Esseen boundsmultiple Wiener-Itô integralsGaussian approximationfourth moment theoremproduct formulaPoisson functionalscarré-du-champ operator

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 (2)

Stable limit theorems on the Poisson space ⋮ Modified log-Sobolev inequalities, Beckner inequalities and moment estimates

Cites Work

• Unnamed Item
• Quantitative de Jong theorems in any dimension
• Poisson process Fock space representation, chaos expansion and covariance inequalities
• Stochastic analysis in discrete and continuous settings. With normal martingales.
• Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization
• The fourth moment theorem on the Poisson space
• Quantitative CLTs for symmetric \(U\)-statistics using contractions
• Fourth moment theorems on the Poisson space in any dimension
• Normal Approximations with Malliavin Calculus
• Stochastic Analysis for Poisson Processes

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