论文标题
平均野外游戏中主方程的分裂方法和短时间存在
Splitting methods and short time existence for the master equations in mean field games
论文作者
论文摘要
我们开发了一种分裂方法，以在短时间内证明平均野外游戏（MFG）中两个主方程的解决方案的适合性：二阶主方程，描述具有共同噪声的MFG，以及与MFG与MFG相关联的MASTER方程系统。这两个问题都是在概率度量空间中所述的无限尺寸方程。我们的新方法简化，缩短和概括了二阶主方程的先前存在结果，并为与主要参与者相关的MFG问题提供了第一个存在结果。
We develop a splitting method to prove the well-posedness, in short time, of solutions for two master equations in mean field game (MFG) theory: the second order master equation, describing MFGs with a common noise, and the system of master equations associated with MFGs with a major player. Both problems are infinite dimensional equations stated in the space of probability measures. Our new approach simplifies, shortens and generalizes previous existence results for second order master equations and provides the first existence result for systems associated with MFG problems with a major player.
