A note on Monge–Kantorovich problem

Pengbin Feng and Xuhui Peng

Statistics & Probability Letters, 2014, vol. 84, issue C, 204-211

Abstract: Shen and Zheng (2010) and Xu and Yan (2013) considered the Monge–Kantorovich problem in the plane and proved that the optimal coupling for the problem has a form (X1,g(X1,Y2), h(X1,Y2),Y2), and then they assumed (X1,Y2) has a density p and gave the equation which p should satisfy. In this article, we prove that (X1,Y2) naturally has a density under more weak conditions. We again prove a similar result in dimension 3 and give an exact form (X1,g1(X1,Y2,Y3), g2(X1,Y2,Y3),h(X1,Y2,Y3),Y2,Y3) depending on a certain convex function.

Keywords: Monge–Kantorovich problem; Optimal transportation; Partial differential equations (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715213003544
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:84:y:2014:i:c:p:204-211

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2013.10.011

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().