Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition
Author(s)Antunović, Tonći; Peres, Yuval; Sheffield, Scott Roger; Somersille, Stephanie
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We study a version of the stochastic “tug-of-war” game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function is shifted by an appropriate constant, the values of the game after n steps converge in the continuous case and the case of finite graphs with loops. Using this we prove the existence of solutions to the infinity Laplace equation with vanishing Neumann boundary condition.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Communications in Partial Differential Equations
Taylor & Francis
Antunović, Tonći, Yuval Peres, Scott Sheffield, and Stephanie Somersille. “Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition.” Communications in Partial Differential Equations 37, no. 10 (October 2012): 1839-1869.