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Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals

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Rachev S. T., R. M.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS §0. Introduction...................................................................................................................................5 §1. Notation and terminology..............................................................................................................6 §2. A generalization of the Kantorovich-Rubinstein theorem..............................................................8 §3. Application: explicit representations for a class of probability metrics.........................................14 §4. Topology of the Kantorovich-Rubinstein norm............................................................................18 §5. Dual representation for the Wasserstein functional....................................................................21 §6. Comparison of Wasserstein functional and Kantorovich-Rubinstein norm; completeness..........27 §7. Convergence of empirical measures; results of Fortet-Mourier type..........................................30 §8. The convex set of optimal measures..........................................................................................32 References......................................................................................................................................34

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1 R. M.

1 Rachev S. T.

1 1990

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Duality theorems for Kantorovich-Rubinstein and Wasserstein functionals