Fully Discrete Schemes for the Value Function of Pursuit-Evasion Games

We consider the classical pursuit-evasion problem and an approximation scheme based on Dynamic Programming. We prove the convergence of the scheme to the value function of the game by using some recent results and methods of the theory of viscosity solutions to the Isaacs equations. The more restrictive assumption is the continuity of the value function, but we can eliminate it when dealing with control problems with a single player. We test the algorithm on two simple examples with explicit solution.

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