A constructive approach to the Monge-Kantorovich problem for chains of infinite order
نویسندگان
چکیده
We propose a constructive approach to solve the Monge-Kantorovich problem for chains of infinite order on a finite alphabet with an additive cost function. From this constructive description of the Kantorovich coupling we obtain, for any ǫ > 0, a perfect simulation algorithm for sampling from an ǫ-approximating coupling which assigns to the cost function an expectation which is ǫ-close to the minimum cost. Our approach is based on a regenerative scheme which enable us to construct the Kantorovich coupling as a mixture of product measures.
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