论文标题
Wasserstein Hamiltonian流动，图上有共同噪声
Wasserstein Hamiltonian flow with common noise on graph
论文作者
论文摘要
我们在有限图的密度歧管上研究了瓦斯汀·哈密顿流动的流动。在随机变分原理的框架下，我们首先发展了随机瓦斯汀·汉密尔顿流的制定，并显示出独特的解决方案的局部存在。我们还为解决方案的全球存在建立了足够的条件。因此，我们获得了具有图形上常见噪声的非线性schrödinger方程的全局良好性。此外，使用对公共噪声的Wong-Zakai近似值，我们证明了最小化的最佳控制问题的存在。我们表明，它的最小化器也满足了图形上随机的瓦斯坦·哈密顿的流动。
We study the Wasserstein Hamiltonian flow with a common noise on the density manifold of a finite graph. Under the framework of stochastic variational principle, we first develop the formulation of stochastic Wasserstein Hamiltonian flow and show the local existence of a unique solution. We also establish a sufficient condition for the global existence of the solution. Consequently, we obtain the global well-posedness for the nonlinear Schrödinger equations with common noise on graph. In addition, using Wong-Zakai approximation of common noise, we prove the existence of the minimizer for an optimal control problem with common noise. We show that its minimizer satisfies the stochastic Wasserstein Hamiltonian flow on graph as well.
