On Some Conditions for Strong Law of Large Numbers for Weighted Sums of END Random Variables under Sublinear Expectations

Xiaochen Ma,Qunying Wu

doi:10.1155/2019/7945431

Abstract

In this article, we research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our consequences contain the Kolmogorov strong law of large numbers and the Marcinkiewicz strong law of large numbers for weighted sums of extended negatively dependent random variables. Furthermore, our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context.

Highlights

There are many uncertainties in the fields of economy, statistics, engineering, etc., which cannot be accurately predicted or described by traditional additive probability measures
Our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context
Many uncertain phenomena do not satisfy the linear additivity condition, so the application of classical limit theory is limited to some extent; a growing number of people abnegate the traditional tool of additivity of probability and instead use the new tool of nonadditive probability measure to portray problems with uncertainty

Summary

Introduction

There are many uncertainties in the fields of economy, statistics, engineering, etc., which cannot be accurately predicted or described by traditional additive probability measures. We research some conditions for strong law of large numbers (SLLNs) for weighted sums of extended negatively dependent (END) random variables under sublinear expectation space. Our results extend strong law of large numbers for some sequences of random variables from the traditional probability space to the sublinear expectation space context. The strong law of large numbers for the weighted sums of extended negatively dependent (END) random variables under sublinear expectation has less related results.

Results

Conclusion