Percolation Games
本文引入了一类定义在整数网格上的离散时间随机博弈，作为哈密顿-雅可比方程随机均匀化问题的玩具模型，给出了n阶段博弈值收敛的条件，并讨论了与均匀化理论的联系。
This paper introduces a discrete-time stochastic game class on [Formula: see text], which plays the role of a toy model for the well-known problem of stochastic homogenization of Hamilton–Jacobi equations. Conditions are provided under which the n-stage game value converges as n tends to infinity, and connections with homogenization theory are discussed. Funding: The second author acknowledges the support of the French Agence Nationale de la Recherche (ANR) [Grant ANR-21-CE40-0020] (CONVERGENCE project).