Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 305, Issue -, Pages 428-457Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2021.10.009
Keywords
Wasserstein-Hamiltonian flow; Schrodinger bridge problem; Optimal transport; Time-inhomogeneous
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This article presents a definition of stochastic Hamiltonian process on finite graphs via density dynamics in Wasserstein manifold, demonstrating its existence in classical discrete problems such as the optimal transport problem, Schrodinger equation, and Schrodinger bridge problem. The stationary and periodic properties of Hamiltonian processes are also investigated within the framework of the Schrodinger bridge problem.
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, Schrodinger equation and Schrodinger bridge problem (SBP). The stationary and periodic properties of Hamiltonian processes are also investigated in the framework of SBP. (c) 2021 Elsevier Inc. All rights reserved.
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