论文标题
Wasserstein空间上障碍问题的粘度解决方案
Viscosity solutions for obstacle problems on Wasserstein space
论文作者
论文摘要
本文是我们随附的论文[Talbi，Touzi和Zhang（2021）]的延续，我们在其中表征了概率措施的Wasserstein空间上的障碍物方程的平均场最佳停止问题，前提是价值函数平稳。我们的目的是在较弱的规律性要求下确定此特征。我们应为这种方程式定义粘度解决方案的概念，并证明存在，稳定性和比较原理。
This paper is a continuation of our accompanying paper [Talbi, Touzi and Zhang (2021)], where we characterized the mean field optimal stopping problem by an obstacle equation on the Wasserstein space of probability measures, provided that the value function is smooth. Our purpose here is to establish this characterization under weaker regularity requirements. We shall define a notion of viscosity solutions for such equation, and prove existence, stability, and comparison principle.
