Optimal solution of a Monge-Kantorovitch transportation problem. (English) Zbl 0938.60012
It is well-known that, for any pair \((P,Q)\) of probability measures on a separable Banach space \(({\mathbf E},\|\cdot\|)\), under certain regularity conditions there exists a function \(f:{\mathbf E}\mapsto{\mathbf E}\) such that \(f(X)\) has the distribution \(Q\) and the pair \((X,f(X))\) is an optimal coupling for the so-called Monge-Kantorovich problem. An approximation of the function \(f\) is given when the distribution \(Q\) is discrete. An extention of this result to a general distribution \(Q\) is also considered.
Reviewer: L.Heinrich (Augsburg)
MSC:
| 60B05 | Probability measures on topological spaces |
| 60E05 | Probability distributions: general theory |
| 60F25 | \(L^p\)-limit theorems |
Keywords:
Monge-Kantorovich transportation problem; \(p\)-optimal coupling; Kantorovich metric; optimal solutionReferences:
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