Rates of Convergence in Periodic Homogenization of Nonlocal Hamilton- Jacobi- Bellman Equations

In this paper we provide a rate of convergence for periodic homogenization of Hamilton- Jacobi- Bellman equations with nonlocal diffusion. The result is based on the regularity of the associated effective problem, where convexity plays a crucial role. The necessary regularity estimates are made possible by a representation formula we obtain for the effective Hamiltonian, a result that has an independent interest. © The authors. Published by EDP Sciences, SMAI 2023.