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

## TL;DR

This paper develops a framework for reflected stochastic differential equations driven by G-Brownian motion in non-convex domains, establishing existence, uniqueness, and solution properties using penalization and fixed-point methods.

## Contribution

It introduces a novel approach to define and analyze reflected G-Brownian motion in non-convex domains, extending existing stochastic calculus methods.

## Key findings

- Existence and uniqueness of reflected G-Brownian motion established.
- Penalization method adapted for non-convex domains.
- Multi-dimensional reflected SDEs solved via fixed-point argument.

## 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 $\alpha$-H\"older continuous functions. With the help of these results obtained previously for deterministic problems, we pathwisely define the reflected $G$-Brownian motion and prove its existence and uniqueness in a Banach space. Finally, multi-dimensional reflected stochastic differential equations driven by $G$-Brownian motion are investigated via a fixed-point argument.