On Stein's method for infinite-dimensional Gaussian approximation in abstract Wiener spaces

DOI10.1016/j.jfa.2011.04.016zbMath1221.60110OpenAlexW2083497769MaRDI QIDQ549655

Hsin-Hung Shih

Publication date: 18 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2011.04.016

zbMATH Keywords

Stein's methodabstract Wiener spaceGaussian approximationabstract Wiener measure

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Probabilistic potential theory (60J45) Stochastic calculus of variations and the Malliavin calculus (60H07) Measures and integration on abstract linear spaces (46G12)

Related Items (19)

Approximating dependent rare events ⋮ Donsker's theorem in Wasserstein-1 distance ⋮ Stein's method for multivariate Brownian approximations of sums under dependence ⋮ On the characterization of Brownian bridge measure on the pinned path space over a compact Riemannian manifold ⋮ Bernstein-Jackson inequalities on Gaussian Hilbert spaces ⋮ Diffusive limits of Lipschitz functionals of Poisson measures ⋮ Stein's method, smoothing and functional approximation ⋮ On integration by parts formula and characterization of fractional Ornstein-Uhlenbeck process ⋮ Stein's method, Gaussian processes and palm measures, with applications to queueing ⋮ Covariance representations, \(L^p\)-Poincaré inequalities, Stein's kernels, and high-dimensional CLTs ⋮ Stein's method for diffusive limits of queueing processes ⋮ Unnamed Item ⋮ Integration-by-parts characterizations of Gaussian processes ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ Functional approximations via Stein's method of exchangeable pairs ⋮ Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to \(U\)-statistics and stochastic geometry ⋮ Approximation of Hilbert-valued gaussians on Dirichlet structures ⋮ Stein's method of exchangeable pairs in multivariate functional approximations ⋮ Stein's method for rough paths

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the rate of convergence in the multivariate CLT
• Stein's method on Wiener chaos
• Multivariate normal approximation using Stein's method and Malliavin calculus
• Second order Poincaré inequalities and CLTs on Wiener space
• Sharp inequalities and regularity of heat semigroup on infinite dimensional spaces
• Stein's method for diffusion approximations
• The Ornstein-Uhlenbeck semigroup in an infinite dimensional L\(^2\) setting
• Berry-Esseen estimates in Hilbert space and an application to the law of the iterated logarithm
• Gaussian measures in Banach spaces
• Poisson approximation for dependent trials
• White noise calculus and Fock space
• Stochastic processes and orthogonal polynomials
• Potential theory on Hilbert space
• On seminorms and probabilities, and abstract Wiener spaces
• Gaussian measures on a Banach space
• On Stein’s method for multivariate normal approximation
• On the small balls problem for equivalent Gaussian measures
• An Introduction to Stein's Method
• Parabolic Equations Associated with the Number Operator
• Multivariate normal approximations by Stein's method and size bias couplings
• The Topological Support of Gauss Measure on Hilbert Space
• Quasi-Differentiable Functions on Banach Spaces
• Orthogonal polynomials in Stein's method
• Stochastic Equations in Infinite Dimensions

This page was built for publication: On Stein's method for infinite-dimensional Gaussian approximation in abstract Wiener spaces