Local regularity results for value functions of tug-of-war with noise and running payoff
Eero Ruosteenoja

TL;DR
This paper establishes local regularity properties for value functions of a stochastic game called tug-of-war with noise, and applies these results to viscosity solutions of the inhomogeneous p-Laplace equation, providing new game-theoretic proofs.
Contribution
It proves local Lipschitz continuity and Harnack's inequality for these value functions and connects game theory with PDE regularity results for the p-Laplace equation.
Findings
Proved local Lipschitz continuity of value functions
Established Harnack's inequality for the value functions
Provided game-theoretic proofs for regularity of p-Laplace solutions
Abstract
We prove local Lipschitz continuity and Harnack's inequality for value functions of the stochastic game tug-of-war with noise and running payoff. As a consequence, we obtain game-theoretic proofs for the same regularity properties for viscosity solutions of the inhomogeneous -Laplace equation when .
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