We consider a discrete time analog of $G$-expectations and we prove that in the case where the time step goes to zero the corresponding values converge to the original $G$-expectation. Furthermore we provide error estimates for the convergence rate. This paper is continuation of Dolinsky, Nutz, and Soner (2012). Our main tool is a strong approximation theorem which we derive for general discrete time martingales.
"Numerical schemes for G-Expectations." Electron. J. Probab. 17 1 - 15, 2012. https://doi.org/10.1214/EJP.v17-2284