Squared quadratic Wasserstein distance: optimal couplings and Lions differentiability

DOI10.1051/ps/2020013zbMath1454.90028arXiv1811.07787OpenAlexW3012550932MaRDI QIDQ5140338

Aurélien Alfonsi, Benjamin Jourdain

Publication date: 15 December 2020

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.07787

zbMATH Keywords

differentiabilityWasserstein distanceoptimal transportconvex ordercouplings of probability measures

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Martingales with discrete parameter (60G42) Fréchet and Gateaux differentiability in optimization (49J50) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08) Differentiability questions for infinite-dimensional manifolds (58B10)

Related Items (6)

Monotone Solutions of the Master Equation for Mean Field Games with Idiosyncratic Noise ⋮ Solving mean field rough differential equations ⋮ Dynamical Systems and Hamilton–Jacobi–Bellman Equations on the Wasserstein Space and their L² Representations ⋮ A smooth variational principle on Wasserstein space ⋮ An optimal transport-based characterization of convex order ⋮ An introduction to mean field game theory

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