Quantified Cramér-Wold Continuity Theorem for the Kantorovich Transport Distance

2024/12/13 by Bobkov, Sergey G., Götze, Friedrich
#60E #60F #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2412.10276

Abstract

An upper bound for the Kantorovich transport distance between probability measures on multidimensional Euclidean spaces is given in terms of transport distances between one dimensional projections. This quantifies the Cramér-Wold continuity theorem for the weak convergence of probability measures.

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