Mean-field limit of particle systems, McKean-Vlasov SDE, and Mean-field Games under common noise

• Grant number: 23/14629-0
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: March 01, 2024
• End date: February 24, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Paulo Regis Caron Ruffino
• Grantee: Josué Knorst
• Supervisor: Francesco Russo
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Ecole Nationale Supérieure des Techniques Avancées (ENSTA), France
• Associated to the scholarship: 22/13413-0 - Decomposition of flows in averaging principles and stochastic transport equation, BP.PD

Abstract

We propose the study of a system of particles with moderate mean-field interactions and subject to a common noise. We derive the asymptotic behavior ofthe population, which gives rise to a McKean-Vlasov SDE and an associated stochastic PDE at the density level. We investigate the well-posedness and uniqueness of both equations and explore the quantitative convergence of the empirical measure toward the SPDE density solution. Then, we look into the stochastic optimal control formulation of the associated Mean Field Game in search of solutions to equilibrium for the representation player equation.