On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate
Analysis of PDEs
2024-12-12 v1 Optimization and Control
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.
Keywords
Cite
@article{arxiv.2412.08483,
title = {On Inverse Problems for Mean Field Games with Common Noise via Carleman Estimate},
author = {Qi Lü and Zhonghua Liao},
journal= {arXiv preprint arXiv:2412.08483},
year = {2024}
}