The obstacle problem for the ass="a-plus-plus">p-laplacian via optimal stopping of tug-of-war games

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• 作者：Marta Lewicka ; Juan J. Manfredi
• 关键词：Tug ; of ; war games ; Viscosity solutions ; p ; Laplacian ; Obstacle problem
• 刊名：Probability Theory and Related Fields
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：167
• 期：1-2
• 页码：349-378
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Probability Theory and Stochastic Processes; Theoretical, Mathematical and Computational Physics; Quantitative Finance; Mathematical and Computational Biology; Statistics for Business/Economics/Mathem
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-2064
• 卷排序：167

文摘

We present a probabilistic approach to the obstacle problem for the p-Laplace operator. The solutions are approximated by running processes determined by tug-of-war games plus noise, and letting the step size go to zero, not unlike the case when Brownian motion is approximated by random walks. Rather than stopping the process when the boundary is reached, the value function is obtained by maximizing over all possible stopping times that are smaller than the exit time of the domain.