论文标题
一种概率的方法，用于消失在瓦斯坦斯坦空间上PDE的粘度
A probabilistic approach to vanishing viscosity for PDEs on the Wasserstein space
论文作者
论文摘要
在这项工作中，我们证明了一个类似物，对于概率度量空间的部分微分方程，是欧几里得空间方程已知的经典消失粘度结果。我们的结果尤其允许表明，在经典力学和游戏的各种问题中产生的价值函数可以作为二阶PDE的限制情况。证明方法建立在随机分析参数上，例如允许McKean-Vlasov方程证明弗林德林 - 温泽尔大偏差定理。
In this work we prove an analogue, for partial differential equations on the space of probability measures, of the classical vanishing viscosity result known for equations on the Euclidean space. Our result allows in particular to show that the value function arising in various problems of classical mechanics and games can be obtained as the limiting case of second order PDEs. The method of proof builds on stochastic analysis arguments and allows for instance to prove a Freindlin-Wentzell large deviation theorem for McKean-Vlasov equations.
