On near optimal trajectories for a game associated with the ∞-Laplacian
Abstract
A two-player stochastic differential game representation has recently been obtained for solutions of the equation -∞ u=h in a 2 domain with Dirichlet boundary condition, where h is continuous and takes values in \0\. Under appropriate assumptions, including smoothness of u, the vanishing δ limit law of the state process, when both players play δ-optimally, is identified as a diffusion process with coefficients given explicitly in terms of derivatives of the function u.
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