Optimal transportation plans and convergence in distribution

被引：22

作者：

CuestaAlbertos, JA ^{[1
]}

Matran, C ^{[1
]}

TueroDiaz, A ^{[1
]}

机构：

[1] UNIV VALLADOLID, VALLADOLID, SPAIN

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 1997年 / 60卷 / 01期

关键词：

Wasserstein distance; Monge-Kantorovich transportation problem; optimal transportation plans; convergence in distribution; consistency; maximal monotone operators; monotone dependence; Skorohod almost sure representation;

D O I：

10.1006/jmva.1996.1627

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Explicit expression of mappings optimal transportation plans for the Wasserstein distance in R(p), p>1, are not generally available. Therefore, it is of great interest to provide results which justify the practical use of simulation techniques to obtain approximate optimal transportation plans. This is done in this paper, where we obtain the consistency of the empirical optimal transportation plans. Our results can also be employed to justify a definition of multidimensional complete dependence. (C) 1997 Academic Press.

引用

页码：72 / 83

页数：12

共 15 条

[1]

AURENHAMMER F, 1992, MINKOWSKI TYPE THEOR

[2] NOTES ON THE WASSERSTEIN METRIC IN HILBERT-SPACES [J].