Connections between coupling and Ishii-Lions methods for tug-of-war with noise stochastic games

TL;DR

This paper explores the relationship between the coupling and Ishii-Lions methods in the analysis of stochastic games and viscosity solutions, providing a unified perspective on regularity techniques.

Contribution

It establishes connections between two different regularity methods within the contexts of tug-of-war with noise stochastic games and viscosity solutions of the p-Laplace equation.

Findings

Unified framework for coupling and Ishii-Lions methods

Insights into regularity properties of stochastic games

Potential applications to PDE regularity theory

Abstract

We present a streamlined account of two different regularity methods as well as their connections. We consider the coupling method in the context of tug-of-war with noise stochastic games, and consider viscosity solutions of the $p$-Laplace equation in the context of the Ishii-Lions method.