What is a stochastic Hamiltonian process on finite graph? An optimal transport answer

Jianbo Cui, Shu Liu, Haomin Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)


We present a definition of stochastic Hamiltonian process on finite graph via its corresponding density dynamics in Wasserstein manifold. We demonstrate the existence of stochastic Hamiltonian process in many classical discrete problems, such as the optimal transport problem, Schrödinger equation and Schrödinger bridge problem (SBP). The stationary and periodic properties of Hamiltonian processes are also investigated in the framework of SBP.

Original languageEnglish
Pages (from-to)428-457
Number of pages30
JournalJournal of Differential Equations
Publication statusPublished - 25 Dec 2021


  • Optimal transport
  • Schrödinger bridge problem
  • Time-inhomogeneous Markov process
  • Wasserstein-Hamiltonian flow

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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