Approximation rate in Wasserstein distance of probability measures on the real line by deterministic empirical measures

DOI10.1016/j.jat.2021.105684zbMath1481.60007arXiv2012.09729OpenAlexW3111759905MaRDI QIDQ2071757

Benjamin Jourdain, O. Bencheikh

Publication date: 31 January 2022

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.09729

zbMATH Keywords

rate of convergenceWasserstein distancedeterministic empirical measures

Mathematics Subject Classification ID

Computational methods for problems pertaining to probability theory (60-08) Best approximation, Chebyshev systems (41A50) Approximations to statistical distributions (nonasymptotic) (62E17) Approximation with constraints (41A29) Spaces of measures, convergence of measures (28A33) Convergence of probability measures (60B10) Rate of convergence, degree of approximation (41A25)

Related Items (2)

Vlasov equations on digraph measures ⋮ Weak and strong error analysis for mean-field rank-based particle approximations of one-dimensional viscous scalar conservation laws

Cites Work

• Optimal convergence rate of the multitype sticky particle approximation of one-dimensional diagonal hyperbolic systems with monotonic initial data
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• Central limit theorems for the Wasserstein distance between the empirical and the true distributions
• Foundations of quantization for probability distributions
• Support points
• Best finite constrained approximations of one-dimensional probabilities
• Asymptotic analysis of a class of optimal location problems
• Uniform decomposition of probability measures: quantization, clustering and rate of convergence
• Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances

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