In this paper, we propose a monotone approximation scheme for a class of fully nonlinear degenerate partial integro-differential equations (PIDEs) which characterize the nonlinear $\alpha$-stable L\'{e}vy processes under sublinear expectation space with $\alpha \in(1,2)$. We further establish the error bounds for the monotone approximation scheme. This in turn yields an explicit Berry-Esseen bound and convergence rate for the $\alpha$-stable central limit theorem under sublinear expectation.

翻译：本文针对次线性期望空间中刻画非线性$\alpha$-稳定Lévy过程（$\alpha \in(1,2)$）的一类完全非线性退化偏积分微分方程，提出了一种单调逼近格式。我们进一步建立了该单调逼近格式的误差界，进而得到了次线性期望下$\alpha$-稳定中心极限定理的显式Berry-Esseen界与收敛速率。