Local regularity results for value functions of tug-of-war with noise   and running payoff
  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 $p$-Laplace equation when $p>2$. 
Eero Ruosteenoja
math.AP