[Plenary Lecture] Coupling and Ishii-Lions Methods for Tug-of-War Stochastic Games with Noise

Speaker: Juan Manfredi, University of Pittsburgh

Title: Coupling and Ishii-Lions Methods for Tug-of-War Stochastic Games with Noise

Abstract: We review the theory of viscosity solutions to non-linear elliptic partial differential equations, including the Theorem of Sums. We then provide a detailed exposition of two distinct regularity methodologies and explore their interrelation. We examine the coupling method within the framework of tug-of-war stochastic games augmented by noise and address the regularity of viscosity solutions to the \(p\)-Laplace equation using the Ishii-Lions method. In the first talk, we present relevant definitions, examples, theorems,and further research directions. The details of the proofs will be discussed in the second talk.