Donsker's theorem in Wasserstein-1 distance

DOI10.1214/20-ECP308zbMath1434.60100arXiv1904.07045OpenAlexW3014113681MaRDI QIDQ2183129

Laure Coutin, Laurent Decreusefond

Publication date: 26 May 2020

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

Full work available at URL: https://arxiv.org/abs/1904.07045

zbMATH Keywords

Malliavin calculusStein's methodWasserstein distanceDonsker theorem

Mathematics Subject Classification ID

Gaussian processes (60G15) Strong limit theorems (60F15) Stochastic calculus of variations and the Malliavin calculus (60H07) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (5)

Quantitative control of Wasserstein distance between Brownian motion and the Goldstein-Kac telegraph process ⋮ Rates of convergence for the number of zeros of random trigonometric polynomials ⋮ Diffusive limits of Lipschitz functionals of Poisson measures ⋮ Stein's method, Gaussian processes and palm measures, with applications to queueing ⋮ Malliavin-Stein method: a survey of some recent developments

Cites Work

• On Stein's method for infinite-dimensional Gaussian approximation in abstract Wiener spaces
• Stein's method for rough paths
• Stein's method for diffusion approximations
• An introduction to analysis on Wiener space
• Multivariate approximations in Wasserstein distance by Stein's method and Bismut's formula
• A multivariate Berry-Esseen theorem with explicit constants
• On the convergence of sums of independent Banach space valued random variables
• The Stein-Dirichlet-Malliavin method
• Multidimensional Stochastic Processes as Rough Paths
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