Hausdorff distances between couplings and optimal transportation

DOI10.4213/sm9920ezbMath1543.49037MaRDI QIDQ6569570

Vladimir I. Bogachev, S. N. Popova

Publication date: 9 July 2024

Published in: Sbornik: Mathematics (Search for Journal in Brave)

zbMATH Keywords

weak convergencecouplingHausdorff distanceMonge problemKantorovich problemcontinuity with respect to parameter

Mathematics Subject Classification ID

Probabilistic measure theory (60A10) Optimal transportation (49Q22)

Related Items (1)

Continuous dependence of sets in a space of measures and a program minimax problem

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Monge problem with vanishing gradient penalization: vortices and asymptotic profile
• Measurable dependence of conditional measures on a parameter
• Continuous selections. I
• On the equality between Monge's infimum and Kantorovich's minimum in optimal mass transportation
• On the continuity of correspondences on sets of measures with restricted marginals
• Mass transportation problems. Vol. 1: Theory. Vol. 2: Applications
• An approximation scheme for the Kantorovich-Rubinstein problem on compact spaces
• A general duality theorem for marginal problems
• Geometry and dynamics of admissible metrics in measure spaces
• Foundations of quantization for probability distributions
• Geometry of Kantorovich polytopes and support of optimizers for repulsive multi-marginal optimal transport on finite state spaces
• Quadratically regularized optimal transport
• An invitation to optimal transport, Wasserstein distances, and gradient flows
• The Kantorovich problem with a parameter and density constraints
• Kantorovich problems with a parameter and density constraints
• Applications of weak transport theory
• Existence of solutions to the nonlinear Kantorovich transportation problem
• Differential inclusions in Wasserstein spaces: the Cauchy-Lipschitz framework
• Entropic regularization of continuous optimal transport problems
• Kantorovich problems and conditional measures depending on a parameter
• Exponential mixing for a class of dissipative PDEs with bounded degenerate noise
• On the equality of values in the Monge and Kantorovich problems
• Existence, duality, and cyclical monotonicity for weak transport costs
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Kantorovich duality for general transport costs and applications
• Limit theorems in Wasserstein distance for empirical measures of diffusion processes on Riemannian manifolds
• On Kantorovich problems with a parameter
• Kantorovich type topologies on spaces of measures and convergence of barycenters
• Parametrized Kantorovich-Rubinštein theorem and application to the coupling of random variables
• The Monge-Kantorovich problem: achievements, connections, and perspectives
• Weak Convergence of Measures
• Lectures on Optimal Transport
• A new class of costs for optimal transport planning
• One-dimensional empirical measures, order statistics, and Kantorovich transport distances
• Stochastic Monge–Kantorovich problem and its duality
• A Selection Theorem
• Correction to "On real-valued functions in topological spaces"
• Optimal Transport
• Kantorovich problem of optimal transportation of measures: new directions of research

This page was built for publication: Hausdorff distances between couplings and optimal transportation