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

Piermarco Cannarsa; Cristian Mendico

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arXiv · 2402.11521

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

Piermarco Cannarsa·Cristian Mendico

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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 $\varepsilon$.

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Piermarco Cannarsa, Cristian Mendico. 2024-02-18. Rate of convergence for first-order singular perturbation problems: Hamilton-Jacobi-Isaacs equations and mean field games of acceleration. https://arxiv.org/abs/2402.11521

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