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arXiv · 2406.18404

Stochastic Homogenization of HJ Equations: a Differential Game Approach

Andrea Davini·Raimundo Saona·Bruno Ziliotto
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Abstract

We prove stochastic homogenization for a class of non-convex and non-coercive 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.

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Andrea Davini, Raimundo Saona, Bruno Ziliotto. 2024-06-26. Stochastic Homogenization of HJ Equations: a Differential Game Approach. https://arxiv.org/abs/2406.18404

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