A weighted central limit theorem under sublinear expectations

TL;DR

This paper extends the classical central limit theorem to weighted sums of independent random variables within the framework of sublinear expectations, broadening the scope of probabilistic limit theorems.

Contribution

It introduces a weighted central limit theorem under sublinear expectations, generalizing previous results by Peng, Li, and Shi.

Findings

Established a new CLT for weighted sums under sublinear expectations

Extended classical results to a more general expectation framework

Provided theoretical foundation for further research in nonlinear probability

Abstract

In this paper, we investigate a central limit theorem for weighted sums of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng and Li and Shi.