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

TL;DR

This paper develops a monotone approximation scheme for nonlinear PIDEs related to $ ext{alpha}$-stable Levy processes under sublinear expectation, providing explicit convergence rates and Berry-Esseen bounds for the associated central limit theorem.

Contribution

It introduces a novel approximation scheme for nonlinear PIDEs in sublinear expectation spaces and derives explicit convergence rates for the $ ext{alpha}$-stable CLT.

Findings

Established error bounds for the approximation scheme

Derived explicit Berry-Esseen bounds

Quantified convergence rates for the $ ext{alpha}$-stable CLT

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 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.