Note on the optimal transportation of distributions |
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Authors: | C. S. Smith M. Knott |
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Affiliation: | (1) Department of Statistics, London School of Economics, London, England |
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Abstract: | We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property. |
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Keywords: | Marginal distributions cyclic monotonicity subgradient mappings |
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