Transportation costs for optimal and triangular transformations of Gaussian measures

Dmitry B. Bukin, Elena P. Krugova
Theory of Stochastic Processes
Vol.23 (39), no.2, 2018, pp.21-32
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.