论文标题
McKean-Vlasov控制的粘度解决方案
Viscosity Solutions for McKean-Vlasov Control on a torus
论文作者
论文摘要
研究了使用内在线性导数定义的相应动态编程方程的概率度量方程中的最佳控制问题。相对于一种新型光滑的傅立叶度量，该值函数表明是Lipschitz的连续。 Lipschitz粘度子和动态编程方程的超级解决方案之间的比较结果证明了该指标被证明，将值函数描述为独特的Lipschitz粘度解决方案。
An optimal control problem in the space of probability measures, and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a novel smooth Fourier Wasserstein metric. A comparison result between the Lipschitz viscosity sub and super solutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.
