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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:129

Article

Shao, Jinghai¹ 

[1] Tianjin Univ, Ctr Appl Math, Tianjin 300072, Peoples R China

关键词: Monge-Kantorovich problem;    Path groups;    Loop groups;    Heat kernel measure;    Pinned Wiener measure;   

DOI  :  10.1016/j.spa.2018.02.009

来源: Elsevier

【 摘 要 】

In this work we prove the existence and uniqueness of the optimal transport map for L-P-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. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free