In this talk, we are concerned with game-theoretic approaches to several types of PDEs.
Probabilistic methodology has been used as a powerful tool to study PDEs in recent decades. It not only provides a different perspective to comprehend PDEs but also contributes to leading to new mathematical discoveries.
It is well-known about the association between the Laplacian and random walk processes. In this discussion, the mean value property of harmonic functions is a key property. We can also consider similar approaches to more general equations.
For nonlinear cases, 'tug-of-war' is a representative example in this respect, which is a discretized scheme for the normalized p-Laplace operator. Recently, game theoretic approaches have been actively studied for other nonlinear PDEs.