The existence of geodesics in Wasserstein spaces over path groups and loop groups

Jinghai Shao

Stochastic Processes and their Applications, 2019, vol. 129, issue 1, 153-173

Abstract: In this work we prove the existence and uniqueness of the optimal transport map for Lp-Wasserstein distance with p>1, and particularly present an explicit expression of the optimal transport map for the case p=2. As an application, we show the existence of geodesics connecting probability measures satisfying suitable condition on path groups and loop groups.

Keywords: Monge–Kantorovich problem; Path groups; Loop groups; Heat kernel measure; Pinned Wiener measure (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414918300267
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:spapps:v:129:y:2019:i:1:p:153-173

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

DOI: 10.1016/j.spa.2018.02.009

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().