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).
"Stochastic differential equations driven by $G$-Brownian motion with reflecting boundary conditions." Electron. J. Probab. 18 1 - 23, 2013. https://doi.org/10.1214/EJP.v18-2566