RT info:eu-repo/semantics/article
T1 Central limit theorems for general transportation costs
A1 del Barrio, Eustasio
A1 González-Sanz, Alberto
A1 Loubes, Jean-Michel
K1 Estadística
K1 Probabilidad
K1 Optimal transport; Banach–Saks property; CLT; Efron–Stein’s inequality; Cesàro means
AB 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.
SN 0246-0203
YR 2024
FD 2024
LK https://uvadoc.uva.es/handle/10324/82398
UL https://uvadoc.uva.es/handle/10324/82398
LA spa
NO Annales de l’Institut Henri Poincaré – Probablités & Statististique. 60(2): 847-873.
NO Producción Científica
DS UVaDOC
RD 30-ene-2026