A game-theoretic approach to the parabolic normalized p-Laplacian obstacle problem
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917050100744192 |
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| author | Bahja, Hamid El |
| author_facet | Bahja, Hamid El |
| contents | This paper establishes a probabilistic representation for the solution of the parabolic obstacle problem associated with the normalized $p$-Laplacian. We introduce a zero-sum stochastic tug-of-war game with noise in a space-time cylinder, where one player has the option to stop the game at any time to collect a payoff given by an obstacle function. We prove that the value functions of this game exist, satisfy a dynamic programming principle, and converge uniformly to the unique viscosity solution of the continuous obstacle problem as the step size $\varepsilon$ tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25999 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A game-theoretic approach to the parabolic normalized p-Laplacian obstacle problem Bahja, Hamid El Probability Analysis of PDEs 5B65, 47G20, 31B05 This paper establishes a probabilistic representation for the solution of the parabolic obstacle problem associated with the normalized $p$-Laplacian. We introduce a zero-sum stochastic tug-of-war game with noise in a space-time cylinder, where one player has the option to stop the game at any time to collect a payoff given by an obstacle function. We prove that the value functions of this game exist, satisfy a dynamic programming principle, and converge uniformly to the unique viscosity solution of the continuous obstacle problem as the step size $\varepsilon$ tends to zero. |
| title | A game-theoretic approach to the parabolic normalized p-Laplacian obstacle problem |
| topic | Probability Analysis of PDEs 5B65, 47G20, 31B05 |
| url | https://arxiv.org/abs/2510.25999 |