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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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Abstract
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.
Date issued
2012-10
URI
http://hdl.handle.net/1721.1/81194
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Communications in Partial Differential Equations
Publisher
Taylor & Francis
Citation
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.
Version: Original manuscript
ISSN
0360-5302
1532-4133

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