Tug-of-war and infinity Laplace equation with vanishing Neumann boundary\n condition

2011/09/22 by Tonći Antunović, Yuval Peres, Antunović, Tonći +5
Economics, Econometrics and Finance · Mathematics · #35J70 #91A15 #91A24 #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Statistical Research #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1109.4918

openalex publication_date 2011/09/22 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We study a version of the stochastic "tug-of-war" game, played on graphs and\nsmooth domains, with the empty set of terminal states. We prove that, when the\nrunning payoff function is shifted by an appropriate constant, the values of\nthe game after n steps converge in the continuous case and the case of finite\ngraphs with loops. Using this we prove the existence of solutions to the\ninfinity Laplace equation with vanishing Neumann boundary condition.\n

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