The obstacle problem for the p-laplacian via optimal stopping of\n Tug-of-War games

2014/11/19 by Marta Lewicka, Lewicka, Marta, Juan J. Manfredi +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1411.5421

openalex publication_date 2014/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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