Mean rates of convergence of empirical measures in the Wasserstein metric

DOI10.1016/0377-0427(94)90033-7zbMath0819.60031OpenAlexW2037092210MaRDI QIDQ1891042

Joseph Horowitz, Rajeeva L. Karandikar

Publication date: 21 August 1995

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90033-7

zbMATH Keywords

rate of convergencediffusionspropagation of chaosempirical measurediffusions with jumpsmean square Wasserstein distance

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Exchangeability for stochastic processes (60G09)

Related Items (22)

Convergence and finite sample approximations of entropic regularized Wasserstein distances in Gaussian and RKHS settings ⋮ Some recent developments in functional inequalities ⋮ Backward propagation of chaos ⋮ Approximation by finitely supported measures ⋮ Constructive quantization: approximation by empirical measures ⋮ From the master equation to mean field game limit theory: large deviations and concentration of measure ⋮ Regularity of the value function and quantitative propagation of chaos for mean field control problems ⋮ Empirical approximation to invariant measures for McKean-Vlasov processes: mean-field interaction vs self-interaction ⋮ Sequential propagation of chaos for mean-field BSDE systems ⋮ Inference for Empirical Wasserstein Distances on Finite Spaces ⋮ Classification on Large Networks: A Quantitative Bound via Motifs and Graphons (Research) ⋮ Rates of convergence for partial mass problems ⋮ Deconvolution for the Wasserstein metric and geometric inference ⋮ On the mean speed of convergence of empirical and occupation measures in Wasserstein distance ⋮ On the rate of convergence in Wasserstein distance of the empirical measure ⋮ Empirical optimal transport on countable metric spaces: distributional limits and statistical applications ⋮ Risk-sensitive mean field games via the stochastic maximum principle ⋮ Multivariate goodness-of-fit tests based on Wasserstein distance ⋮ Uniform rates of the Glivenko-Cantelli convergence and their use in approximating Bayesian inferences ⋮ Path independence of the additive functionals for McKean–Vlasov stochastic differential equations with jumps ⋮ Simultaneous inference for autocovariances based on autoregressive sieve bootstrap ⋮ Finite Sample Approximations of Exact and Entropic Wasserstein Distances Between Covariance Operators and Gaussian Processes

Cites Work

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• Calcul stochastique et problèmes de martingales
• On Pseudomoments
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules
• Mass transhipment problems and ideal metrics
• The Speed of Mean Glivenko-Cantelli Convergence

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