Tug-of-war games with varying probabilities and the normalized $p(x)$-Laplacian

Abstract

We study a tug-of-war game with varying probabilities. In particular, we show that the value of the game is locally asymptotically Hölder continuous. We also show the existence and uniqueness of values of the game. As an application, we prove that the value function of the game converges to a solution of the normalized $p(x)$-Laplacian.

31 pages

References in corpus (2)

• Hölder continuity and bounds for fundamental solutions to non-divergence form parabolic equations
• Harnack's inequality for p-harmonic functions via stochastic games

Cited by in corpus (5)

• Local Lipschitz regularity for functions satisfying a time-dependent dynamic programming principle
• Convergence of dynamic programming principles for the $p$-Laplacian
• Time-dependent tug-of-war games and normalized parabolic $p$-Laplace equations
• Game-theoretic approach to Hölder regularity for PDEs involving eigenvalues of the Hessian
• $p$-harmonic functions by way of intrinsic mean value properties