标题： 关于通过Carleman估计求解具有共同噪声的平均场博弈的逆问题 显示英文标题

标题： On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate

摘要： 在本文中，我们研究了具有共同噪声的平均场博弈（MFGs）的两种逆问题。 我们的重点是由随机汉密尔顿-雅可比-贝尔曼方程和福克-普朗克方程耦合系统描述的MFGs。 首先，我们基于密度函数的终端观测，建立了确定随机汉密尔顿-雅可比-贝尔曼方程和福克-普朗克方程耦合系统解的Lipschitz和Hölder稳定性。 其次，我们推导了与所考虑系统相关的逆源问题的唯一性定理。 建立这些结果的主要工具是两个新的Carleman估计。 显示英文摘要

摘要： In this paper, we study two kinds of inverse problems for Mean Field Games (MFGs) with common noise. Our focus is on MFGs described by a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations. Firstly, we establish the Lipschitz and H\"older stability for determining the solutions of a coupled system of stochastic Hamilton-Jacobi-Bellman and Fokker-Planck equations based on terminal observation of the density function. Secondly, we derive a uniqueness theorem for an inverse source problem related to the system under consideration. The main tools to establish those results are two new Carleman estimates.