Hopf-Cole transformation via generalized Schrodinger bridge problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:274

Article

Leger, Flavien¹  Li, Wuchen² 

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90024 USA

[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA

关键词: Hopf-Cole transformation;    Optimal transport;    Wasserstein Symplectic geometry;   

DOI  :  10.1016/j.jde.2020.10.029

来源: Elsevier

【 摘 要 】

We study generalized Hopf-Cole transformations motivated by the Schrddinger bridge problem, which can be seen as a boundary value Hamiltonian system on the Wasserstein space. We prove that generalized Hopf-Cole transformations are symplectic submersions in the Wasserstein symplectic geometry. Based on this transformation, energy splitting inequalities are provided. Published by Elsevier Inc.

【 授权许可】

Free