Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition
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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Taylor & Francis
2013
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| Online Access: | http://hdl.handle.net/1721.1/81194 https://orcid.org/0000-0002-5951-4933 |
| _version_ | 1811068274610274304 |
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| author | Antunović, Tonći Peres, Yuval Sheffield, Scott Roger Somersille, Stephanie |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Antunović, Tonći Peres, Yuval Sheffield, Scott Roger Somersille, Stephanie |
| author_sort | Antunović, Tonći |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T07:53:53Z |
| format | Article |
| id | mit-1721.1/81194 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T07:53:53Z |
| publishDate | 2013 |
| publisher | Taylor & Francis |
| record_format | dspace |
| spelling | mit-1721.1/811942022-09-23T09:29:12Z Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition Antunović, Tonći Peres, Yuval Sheffield, Scott Roger Somersille, Stephanie Massachusetts Institute of Technology. Department of Mathematics Sheffield, Scott Roger 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. National Science Foundation (U.S.) (NSF grant DMS-0636586) 2013-09-26T15:27:03Z 2013-09-26T15:27:03Z 2012-10 2011-10 Article http://purl.org/eprint/type/JournalArticle 0360-5302 1532-4133 http://hdl.handle.net/1721.1/81194 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. https://orcid.org/0000-0002-5951-4933 en_US http://dx.doi.org/10.1080/03605302.2011.642450 Communications in Partial Differential Equations Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Taylor & Francis arXiv |
| spellingShingle | Antunović, Tonći Peres, Yuval Sheffield, Scott Roger Somersille, Stephanie Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition |
| title | Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition |
| title_full | Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition |
| title_fullStr | Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition |
| title_full_unstemmed | Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition |
| title_short | Tug-of-War and Infinity Laplace Equation with Vanishing Neumann Boundary Condition |
| title_sort | tug of war and infinity laplace equation with vanishing neumann boundary condition |
| url | http://hdl.handle.net/1721.1/81194 https://orcid.org/0000-0002-5951-4933 |
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