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：本文旨在通过数值方法研究次线性期望下$α$-稳定中心极限定理的误差估计，其中$α \in(0,2)$，其极限分布可由一个完全非线性积分-微分方程（PIDE）描述。基于独立随机变量序列，我们为该完全非线性PIDE提出了一种离散逼近格式。借助非线性随机分析技术和数值分析工具，我们建立了离散逼近格式的误差界，进而为稳健$α$-稳定中心极限定理提供了通用误差界，包括可积情形$α \in(1,2)$和不可积情形$α \in(0,1]$。最后，我们提供具体算例来说明主要结果并推导精确收敛速度。