In this paper, we propose a class of discrete-time approximation schemes for fully nonlinear Hamilton-Jacobi-Bellman (HJB) equations associated with stochastic optimal control problems under the $G$-expectation framework. We prove the convergence of the discrete schemes and determine the convergence rate. Several numerical examples are presented to illustrate the effectiveness of the obtained results.

翻译：在本文中,我们建议为完全非线性汉密尔顿-Jacobi-Bellman(HJB)等式制定一类离散时间近似计划,这些等式与G$预期框架下的随机最佳控制问题相关,我们证明离散计划趋同,并确定趋同率。