Tug of war games and applications to pdes 1

The fundamental works of Doob, Hunt, Kakutani, Kolmogorov, Lévy and many others have shown a powerful connection between the classical linear potential theory and the corresponding probability theory. The idea behind the classical interplay is that harmonic functions and martingales share a common origin in mean value properties. This approach turns out to be useful in the nonlinear theory as well. This talk introduces basic theory of tug-of-war games and their connection to p-harmonic functions.