论文标题
在状态空间的不变条件下，有限域中的主方程
The Master Equation in a Bounded Domain under Invariance Conditions for the State Space
论文作者
论文摘要
在本文中，我们研究了在不变性型条件下平均野外游戏的主方程的适合性（存在和唯一性），也称为受控动力学的可行性条件。相关平均场游戏系统的解决方案的内部规律性及其线性化版本（在存在证明中起着至关重要的作用）是通过在Neumann边界情况情况下的相应解决方案的全局规则性获得的。最后，我们证明相关NASH系统的解决方案会收敛到主方程的解决方案。
In this paper, we study the well-posedness (existence and uniqueness) of the Master Equation of Mean Field Games under invariance-type conditions, otherwise known as viability conditions for the controlled dynamics. The interior regularity of the solutions of the associated Mean Field Game system and its linearized version, which plays a crucial role in the proof of the existence, is obtained by the global regularity of the corresponding solutions in the Neumann boundary conditions case. Finally, we prove that the solution of the related Nash system converges to the solution of the Master Equation.
