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arXiv · 2412.08483

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

Qi Lü·Zhonghua Liao
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Abstract

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.

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Qi Lü, Zhonghua Liao. 2024-12-11. On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate. https://arxiv.org/abs/2412.08483

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