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In this paper we provide a rate of convergence for periodic homogenization ofHamilton-Jacobi-Bellman equations with nonlocal diffusion. The result is basedon the regularity of the associated effective problem, where the convexityplays a crucial role. Such regularity estimates are possible from the availableliterature once we provide a representation formula for the effectiveHamiltonian, a result that has an independent interest.

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