Generalization of the Nualart-Peccati criterion

DOI10.1214/14-AOP992zbMath1342.60026arXiv1305.6579OpenAlexW1755329620MaRDI QIDQ282494

Guillaume Poly, Dominique Malicet, Guillaume Mijoule, Ehsan Azmoodeh

Publication date: 12 May 2016

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.6579

zbMATH Keywords

spectral theoryHermite polynomialsmoment inequalitiesWiener chaosfourth moment theorem\(\Gamma\)-calculusMarkov diffusive generatorsmultiple Wiener-Itō integralsNualart-Peccati criterion

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Markov semigroups and applications to diffusion processes (47D07) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General spectral theory of ordinary differential operators (34L05) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (13)

Optimal Gamma Approximation on Wiener Space ⋮ Classical and free fourth moment theorems: universality and thresholds ⋮ Quantitative clts on a gaussian space: a survey of recent developments ⋮ The fourth moment theorem on the Poisson space ⋮ High-dimensional central limit theorems for homogeneous sums ⋮ Multidimensional limit theorems for homogeneous sums: A survey and a general transfer principle ⋮ Squared chaotic random variables: new moment inequalities with applications ⋮ Stein operators for variables form the third and fourth Wiener chaoses ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ On a new Sheffer class of polynomials related to normal product distribution ⋮ Stein characterizations for linear combinations of gamma random variables ⋮ Stein's method, logarithmic Sobolev and transport inequalities ⋮ Generalizations of the fourth moment theorem

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