This article is cited in 1 paper

Transportation costs for optimal and triangular transformations of Gaussian measures

Dmitry V. Bukin^a, Elena P. Krugova<sup>b

a</sup> Department of Mechanics and Mathematics, Moscow State University, Moscow 119991, Russia
^b Russian Institute for Scientific and Technical Information, Usievicha 20, Moscow 125190, Russia

Abstract: 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.

MSC: 28C20; 46G12; 60G15

Language: English