What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
What is a stochastic Hamiltonian process on finite graph? An optimal transport answer
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DOI：
10.1016/j.jde.2021.10.009
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发表时间：
2021-01
影响因子：
2.4
通讯作者：
J. Cui;Shu Liu;Haomin Zhou
中科院分区：
文献类型：
--
作者：
J. Cui;Shu Liu;Haomin Zhou
通过Wasserstein流形上随机Hamilton过程的密度动力学，给出了有限图上随机Hamilton过程的定义。我们证明了许多经典离散问题，如最优输运问题、薛定谔方程和薛定谔桥问题（SBP）中随机Hamilton过程的存在性。在SBP框架下研究了哈密顿过程的平稳性和周期性。
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.