Approximation of Hilbert-valued gaussians on Dirichlet structures

DOI10.1214/20-EJP551zbMath1480.46057arXiv1905.05127MaRDI QIDQ2042648

Solesne Bourguin, Simon Campese

Publication date: 21 July 2021

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

Full work available at URL: https://arxiv.org/abs/1905.05127

zbMATH Keywords

functional limit theoremsGaussian approximationprobabilistic metricsGaussian measures on Hilbert spacesDirichlet structuresfourth moment conditionsStein's method on Banach spaces

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17) Measures and integration on abstract linear spaces (46G12) Applications of functional analysis in probability theory and statistics (46N30) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (10)

High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices ⋮ Diffusive limits of Lipschitz functionals of Poisson measures ⋮ Stein's method, smoothing and functional approximation ⋮ Spherical Poisson waves ⋮ 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 ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ Stein's method for the Poisson-Dirichlet distribution and the Ewens sampling formula, with applications to Wright-Fisher models ⋮ Stein's method of exchangeable pairs in multivariate functional approximations ⋮ The multivariate functional de Jong CLT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multivariate Gaussian approximations on Markov chaoses
• Strong and weak approximation of semilinear stochastic evolution equations
• On the Gaussian approximation of vector-valued multiple integrals
• Quantitative Breuer-Major theorems
• On Stein's method for infinite-dimensional Gaussian approximation in abstract Wiener spaces
• Dirichlet forms and symmetric Markov processes.
• Chaos of a Markov operator and the fourth moment condition
• Stein's method on Wiener chaos
• Multivariate normal approximation using Stein's method and Malliavin calculus
• Central limit theorems for non-linear functionals of Gaussian fields
• Stein's method for diffusion approximations
• Anticipating Hilbert integrals with respect to a cylindrical Wiener process and associated stochastic calculus
• Dirichlet forms and analysis on Wiener space
• Introduction to the theory of (non-symmetric) Dirichlet forms
• Gaussian measures in Banach spaces
• Stochastic evolution equations with random generators
• Functional approximations via Stein's method of exchangeable pairs
• Continuous Breuer-Major theorem: tightness and nonstationarity
• Stein's method for multivariate Brownian approximations of sums under dependence
• The functional Breuer-Major theorem
• Berry-Esseen bounds in the Breuer-major CLT and Gebelein's inequality
• Four moments theorems on Markov chaos
• Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws
• Fourth moment theorems for Markov diffusion generators
• Central limit theorems for multiple stochastic integrals and Malliavin calculus
• Interest rate models: an infinite dimensional stochastic analysis perspective
• Central limit theorems for sequences of multiple stochastic integrals
• Potential theory on Hilbert space
• Gaussian measures on a Banach space
• Normal Approximations with Malliavin Calculus
• The Malliavin Calculus and Related Topics
• Analysis and Geometry of Markov Diffusion Operators

This page was built for publication: Approximation of Hilbert-valued gaussians on Dirichlet structures