Optimal solution of a Monge-Kantorovitch transportation problem |
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Institution: | Universite Hassan II, Faculté des Sciences Casa I, 8 Route d''el Jodida, BP 5366, Casablanca, Morocco |
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Abstract: | Suppose that P and Q are probabilities on a separable Banach space . It is known that if (P, Q) satisfies certain regularity conditions and a random variable X has law P, then there exists a function , such that the function f(X) has the law Q and the random pair (X, f(X)) is an optimal coupling for the Monge-Kantorovitch problem. In this paper we provide an approximation of the function f when the law Q is discrete. Thenwe extend this main result to any law Q. The proofs are based on a relationship between optimal couplings and nonlinear equations. |
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