A New Central Limit Theorem under Sublinear Expectations

TL;DR

This paper introduces a new framework for sublinear expectations, defining G-distributions and proving a generalized central limit theorem that accounts for mean-uncertainty, extending classical probability results.

Contribution

The paper presents a novel sublinear expectation framework, introduces G-distributions, and establishes a generalized central limit theorem incorporating mean-uncertainty.

Findings

Introduction of G-distributions generalizing G-normal distributions

A new central limit theorem under sublinear expectations

Extension of the law of large numbers to mean-uncertainty cases

Abstract

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a generalization of the law of large number in the case of mean-uncertainty.