Stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions

Abstract

In this paper, we introduce the idea of stochastic integrals with respect to an increasing process in the $G$-framework and extend $G$-Itô's formula. Moreover, we study the solvability of the scalar valued stochastic differential equations driven by $G$ Brownian motion with reflecting boundary conditions (RGSDEs).