Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition
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Sheffield_Tug-of-war and infinity.pdf
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354.86 KB
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Author(s)
Antunović, Tonći
Peres, Yuval
Sheffield, Scott Roger
Somersille, Stephanie
Date Issued
October 2012
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1080/03605302.2011.642450
