Some Types of Convergence for Negatively Dependent Random Variables under Sublinear Expectations

Ruixue Wang,Qunying Wu

doi:10.1155/2019/9037258

Abstract

In this paper, we research complete convergence and almost sure convergence under the sublinear expectations. As applications, we extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space.

Highlights

We extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space
As is well known that limit theorems are important research topics in probability and statistics, classical limit theorems only hold in the case of model certainty
Zhang and Chen [5] established a weighted central limit theorem for independent random variables under sublinear expectation

Summary

Introduction

As is well known that limit theorems are important research topics in probability and statistics, classical limit theorems only hold in the case of model certainty. We research complete convergence and almost sure convergence under the sublinear expectations. We extend some complete and almost sure convergence theorems for weighted sums of negatively dependent random variables from the traditional probability space to the sublinear expectation space. Zhang and Chen [5] established a weighted central limit theorem for independent random variables under sublinear expectation.

Results

Conclusion