We obtain quantitative stochastic homogenization results for Hamilton–Jacobi equations arising in front propagation problems which move in the normal direction with a possible unbounded velocity. More precisely, we establish error estimates and rates of convergence for homogenization and effective Hamiltonian. The main idea is to perturb our unbounded problem by a bounded one, and to establish stability results in this context. Then, we combine the estimates that we find with the ones from the bounded case.

中文翻译：

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无界前向传播问题的定量随机同质化

我们获得了在前向传播问题中出现的 Hamilton-Jacobi 方程的定量随机均匀化结果，这些前向传播问题以可能的无界速度沿法线方向移动。更准确地说，我们为同质化和有效哈密顿量建立了误差估计和收敛速度。主要思想是通过一个有界问题来扰乱我们的无界问题，并在这种情况下建立稳定性结果。然后，我们将我们找到的估计与有界情况的估计结合起来。