CENTRAL LIMIT THEOREMS FOR EMPIRICAL TRANSPORTATION COST IN GENERAL DIMENSION

• 成果类型: Article
• 署名作者: del Barrio, Eustasio; Loubes, Jean-Michel
• 署名单位: Universidad de Valladolid; Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1275
• 发表日期: 2019
• 页码: 926-951
• 关键词: wasserstein distance; CONVERGENCE; asymptotics

摘要

We consider the problem of optimal transportation with quadratic cost between a empirical measure and a general target probability on R-d, with d >= 1. We provide new results on the uniqueness and stability of the associated optimal transportation potentials, namely, the minimizers in the dual formulation of the optimal transportation problem. As a consequence, we show that a CLT holds for the empirical transportation cost under mild moment and smoothness requirements. The limiting distributions are Gaussian and admit a simple description in terms of the optimal transportation potentials.