Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities

摘要

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in omega subset of Double-struck capital R-n. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in omega x omega via couplings.