| Title: | What is a stochastic Hamiltonian process on finite graph? An optimal transport answer | Authors: | Cui, J Liu, S Zhou, H |
Issue Date: | Dec-2021 | Source: | Journal of differential equations, 25 Dec. 2021, v. 305, p. 428-457 | Abstract: | 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. | Keywords: | Wasserstein-Hamiltonian flow Schrodinger bridge problem Optimal transport Time-inhomogeneous Markov process |
Publisher: | Academic Press | Journal: | Journal of differential equations | ISSN: | 0022-0396 | EISSN: | 1090-2732 | DOI: | 10.1016/j.jde.2021.10.009 |
| Appears in Collections: | Journal/Magazine Article |
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