论文标题
平均噪音和退化特质噪声的平均野外游戏
Mean field games with common noise and degenerate idiosyncratic noise
论文作者
论文摘要
我们研究了随机部分微分方程的前向后系统，该方程描述了众多小玩家的平均野外游戏，但受到特质和共同噪声的影响。该问题的独特特征是，特质噪声系数可能会退化，因此系统通常不接收平滑的解决方案。我们为向后的随机汉密尔顿 - 雅各比 - 贝尔曼方程式开发了一个新的弱解决方案概念，并使用它来构建平均野外游戏系统的概率较弱的解决方案。
We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that the idiosyncratic noise coefficient may be degenerate, so that the system does not admit smooth solutions in general. We develop a new notion of weak solutions for backward stochastic Hamilton-Jacobi-Bellman equations, and use this to build probabilistically weak solutions of the mean field game system.
