论文标题
瓦斯恒星空间中部分微分方程的有限维近似
A finite-dimensional approximation for partial differential equations on Wasserstein space
论文作者
论文摘要
本文在概率度量空间上介绍了一类部分微分方程的有限维近似。这些方程在粘度解决方案的意义上得到满足。主要结果指出，有限维PDE的粘度解决方案与Wasserstein空间上PDE的粘度解决方案的粘度解决方案的融合，但前提是后者具有独特性，并且在很大程度上依赖于Barles＆Souganidis单调的适应性，以使我们的上下文中的上下文以及键入量的键入量均可进行键入量。我们以在随机控制和差异游戏中产生的汉密尔顿 - 雅各比 - 贝尔曼和贝尔曼·伊萨克方程的示例来说明这一结果，并提出了对路径依赖性PDE的情况的扩展。
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the convergence of the viscosity solutions of the finite-dimensional PDE to the viscosity solutions of the PDE on Wasserstein space, provided that uniqueness holds for the latter, and heavily relies on an adaptation of the Barles & Souganidis monotone scheme to our context, as well as on a key precompactness result for semimartingale measures. We illustrate this result with the example of the Hamilton-Jacobi-Bellman and Bellman-Isaacs equations arising in stochastic control and differential games, and propose an extension to the case of path-dependent PDEs.
