Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities

Abstract

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega \subset {\mathbb{R}}^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega \times \Omega$ via couplings.

26 pages