Reflected stochastic differential equations driven by G-Brownian motion in non-convex domains

Abstract

In this paper, we first review the penalization method for solving deterministic Skorokhod problems in non-convex domains and establish estimates for problems with [Formula: see text]-Hölder continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected [Formula: see text]-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by [Formula: see text]-Brownian motion are investigated via a fixed-point argument.