2026-05-05T21:57:11Zhttps://uvadoc.uva.es/oai/request

oai:uvadoc.uva.es:10324/823982026-03-11T08:00:27Zcom_10324_1151com_10324_931com_10324_894col_10324_1278

00925njm 22002777a 4500 dc Barrio Tellado, Eustasio del author González Sanz, Alberto author Loubes, Jean-Michel author 2024 We consider the problem of optimal transportation with general cost between an empirical measure and a general target probability on Rd , with d ≥ 1. We provide results on asymptotic stability of optimal transport potentials under minimal regularity assumptions on the costs or the underlying probability. This stability is combined with a refined linearization technique based on the sequential compactness of the closed unit ball in L2(P ) for the weak topology and the strong convergence of Cesàro means along subsequences. As a result we obtain a CLT for the transportation cost under sharp smoothness and moment assumptions, giving a positive answer to a conjecture in (Ann. Probab. 47 (2019) 926–951) for the quadratic costs. Annales de l’Institut Henri Poincaré – Probablités & Statististique. 60(2): 847-873. 0246-0203 https://uvadoc.uva.es/handle/10324/82398 10.1214/22-AIHP1356 847 2 873 Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 60 Estadística Probabilidad Central limit theorems for general transportation costs