A stochastic differential game for the inhomogeneous \(\infty \)-Laplace equation (Q964776)

The authors study a zero-sum stochastic differential game with terminal payoff \(h\in C(\overline G,\mathbb{R}\setminus\{0\})\) and running payoff \(q\in C(\partial G,\mathbb{R})\), where \(G\subset\mathbb{R}^m\) is a bounded \(C^2\) domain. The game is played until the state process exits the domain. The main result establishes a characterization of the game value as the unique viscosity solution \(u\) of the equation \(-2\Delta_\infty u= h\) in \(G\) with boundary data \(q\).