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

TL;DR

This paper establishes convergence rates for periodic homogenization of nonlocal Hamilton-Jacobi-Bellman equations, leveraging regularity estimates derived from a new representation formula for the effective Hamiltonian.

Contribution

It introduces a novel representation formula for the effective Hamiltonian, enabling new regularity estimates crucial for convergence analysis.

Findings

Established a convergence rate for homogenization

Derived regularity estimates from the representation formula

Highlighted the role of convexity in regularity

Abstract

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 the convexity plays a crucial role. Such regularity estimates are possible from the available literature once we provide a representation formula for the effective Hamiltonian, a result that has an independent interest.