Rate of convergence for first-order singular perturbation problems: Hamilton-Jacobi-Isaacs equations and mean field games of acceleration

2024/02/18 by Piermarco Cannarsa, Cannarsa, Piermarco, Cristian Mendico +1 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2402.11521

openalex publication_date 2024/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This work focuses on the rate of convergence for singular perturbation problems for first-order Hamilton-Jacobi equations. As an application we derive the rate of convergence for singularly perturbed two-players zero-sum deterministic differential games (i.e., leading to Hamilton-Jacobi-Isaacs equations) and, subsequently, in case of singularly perturbed mean field games of acceleration. Namely, we show that in both the models the rate of convergence is ε.

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