Geodesic
Transportation costs for optimal and triangular transformations of Gaussian measures
Teoriâ slučajnyh processov, Tome 23 (2018) no. 2, pp. 21-32.

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We study connections between transportation costs (with the quadratic Kantorovich distance) for Monge optimal mappings and increasing triangular mappings between Gaussian measures. We show that the second cost cannot be estimated by the first cost with a dimension-free coefficient, but under certain restrictions a comparison is possible.
Keywords: Gaussian measure, Monge problem, Kantorovich distance, triangular mapping. 
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Dmitry V. Bukin; Elena P. Krugova. Transportation costs for optimal and triangular transformations of Gaussian measures. Teoriâ slučajnyh processov, Tome 23 (2018) no. 2, pp. 21-32. http://geodesic.mathdoc.fr/item/THSP_2018_23_2_a2/

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