In this paper, we propose a monotone approximation scheme for a class of fully nonlinear partial integro-differential equations (PIDEs) which characterize the nonlinear $\alpha$-stable L\'{e}vy processes under sublinear expectation space with $\alpha \in(1,2)$. Two main results are obtained: (i) the error bounds for the monotone approximation scheme of nonlinear PIDEs, and (ii) the convergence rates of a generalized central limit theorem of Bayraktar-Munk for $\alpha$-stable random variables under sublinear expectation. Our proofs use and extend techniques introduced by Krylov and Barles-Jakobsen.

翻译：在本文中,我们建议为一类完全非线性部分内分异方程(PIDEs)提供一个单质近似方案,在亚线性预期空间下的非线性 $\alpha$- sable L\\'{e}vy 进程以$\alpha\ in(1,2)$为特征。主要结果有两个主要:(一) 非线性PIDE单项近似方案的误差界限,以及(二) Bayraktar-Munk 通用中央界限理论在亚线性预期下对$\alpha$- sable L\\'{e}vy 随机变量的趋同率。我们的证据使用和扩展Krylov和Barles-Jakobsen采用的技术。