Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition
Author(s)
Antunović, Tonći; Peres, Yuval; Sheffield, Scott Roger; Somersille, Stephanie
DownloadSheffield_Tug-of-war and infinity.pdf (354.8Kb)
OPEN_ACCESS_POLICY
Open Access Policy
Creative Commons Attribution-Noncommercial-Share Alike
Terms of use
Metadata
Show full item recordAbstract
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
2012-10Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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