On the Gaussian approximation of vector-valued multiple integrals

DOI10.1016/j.jmva.2011.02.001zbMath1274.60072arXiv1009.1310OpenAlexW1971484320MaRDI QIDQ538180

Ivan Nourdin, Salim Noreddine

Publication date: 23 May 2011

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.1310

zbMATH Keywords

cumulantsMalliavin calculuscentral limit theoremmultiple integralsOrnstein-Uhlenbeck semigroup

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stochastic integrals (60H05) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (8)

An Edgeworth expansion for functionals of Gaussian fields and its applications ⋮ The optimal third moment theorem ⋮ Total variation distance between stochastic polynomials and invariance principles ⋮ Convergence of densities of some functionals of Gaussian processes ⋮ Unnamed Item ⋮ Nourdin-Peccati analysis on Wiener and Wiener-Poisson space for general distributions ⋮ Fourth moment theorems on the Poisson space in any dimension ⋮ Approximation of Hilbert-valued gaussians on Dirichlet structures

Cites Work

• Unnamed Item
• Stein's method on Wiener chaos
• Cumulants on the Wiener space
• Multivariate normal approximation using Stein's method and Malliavin calculus
• Multiple stochastic integrals with dependent integrators
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• Central limit theorems for sequences of multiple stochastic integrals
• The Malliavin Calculus and Related Topics
• Stein's method meets Malliavin calculus: a short survey with new estimates

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