On the rate of convergence for an $\alpha$-stable central limit theorem under sublinear expectation

Abstract

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 Lévy 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.

25 pages

References in corpus (1)

• A New Central Limit Theorem under Sublinear Expectations