Stochastic homogenization of HJ equations: A differential game approach

We prove stochastic homogenization for a class of nonconvex and noncoercive first-order Hamilton–Jacobi equations in a finite-range dependence environment for Hamiltonians that can be expressed by a max-min formula. Exploiting the representation of solutions as value functions of differential games, we develop a game-theoretic approach to homogenization. We furthermore extend this result to a class of Lipschitz Hamiltonians that need not admit a global max-min representation. Our methods allow us to get a quantitative convergence rate for solutions with linear initial data toward the corresponding ones of the effective limit problem.