Speaker: Mathieu Lauriere, assistant professor, New York University Shanghai

Date: June 16, 2025

Time: 15:00-16:00 pm

Location: B1238, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Motivated by recent interest in graphon mean field games and their applications this talk provides a comprehensive probabilistic analysis of graphon mean field control (GMFC) problems, where the controlled dynamics are governed by a graphon mean field stochastic differential equation with heterogeneous mean field interactions. We formulate the GMFC problem with general graphon mean field dependence and establish the existence and uniqueness of the associated graphon mean field forward-backward stochastic: differential equations (FBSDEs). We then derive a version of the Pontryagin stochastic maximum principle tailored to GMFC problems. Furthermore, we analyze the solvability of the GMFC problem for linear dynamics and, study the continuity and stability of the graphon mean field FBSDEs under the optimal control profile. Finally, we show that the solution to the GMFC problem provides an approximately optimal solution for large systems with heterogeneous mean field interactions, based on a propagation of chaos result. This is a joint work with Zhongyuan Cao.

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https://www.view.sdu.edu.cn/info/1020/202867.htm