We propose a monotone approximation scheme for a class of fully nonlinear PDEs called G-equations. Such equations arise often in the characterization of G-distributed random variables in a sublinear expectation space. The proposed scheme is constructed recursively based on a piecewise constant approximation of the viscosity solution to the G-equation. We establish the convergence of the scheme and determine the convergence rate with an explicit error bound, using the comparison principles for both the scheme and the equation together with a mollification procedure. The first application is obtaining the convergence rate of Peng's robust central limit theorem with an explicit bound of Berry-Esseen type. The second application is an approximation scheme with its convergence rate for the Black-Scholes-Barenblatt equation.

翻译：我们针对一类完全非线性偏微分方程——G-方程提出了一种单调逼近格式。此类方程常出现在次线性期望空间中G-分布随机变量的刻画中。该格式基于G-方程粘性解的分片常数近似进行递归构造。我们利用格式与方程的比较原理结合磨光方法，证明了格式的收敛性并确定了带有显式误差界的收敛速度。第一个应用是给出彭实戈稳健中心极限定理的收敛速度，该速度具有Berry-Esseen型的显式界。第二个应用是为Black-Scholes-Barenblatt方程提供带收敛速度的逼近格式。