In this work, we develop a numerical method to study the error estimates of the $\alpha$-stable central limit theorem under sublinear expectation with $\alpha \in(0,2)$, whose limit distribution can be characterized by a fully nonlinear integro-differential equation (PIDE). Based on the sequence of independent random variables, we propose a discrete approximation scheme for the fully nonlinear PIDE. With the help of the nonlinear stochastic analysis techniques and numerical analysis tools, we establish the error bounds for the discrete approximation scheme, which in turn provides a general error bound for the robust $\alpha$-stable central limit theorem, including the integrable case $\alpha \in(1,2)$ as well as the non-integrable case $\alpha \in(0,1]$. Finally, we provide some concrete examples to illustrate our main results and derive the precise convergence rates.

翻译：本文中，我们发展了一种数值方法，研究次线性期望下$\alpha \in(0,2)$的$\alpha$-稳定中心极限定理的误差估计，其极限分布可由一个完全非线性积分微分方程(PIDE)刻画。基于独立随机变量序列，我们提出了完全非线性PIDE的离散近似格式。借助非线性随机分析技术与数值分析工具，我们建立了该离散近似格式的误差界，这进而为鲁棒$\alpha$-稳定中心极限定理提供了通用误差界，涵盖了可积情形$\alpha \in(1,2)$以及不可积情形$\alpha \in(0,1]$。最后，我们给出具体实例说明主要结果，并推导出精确的收敛速度。