Exponential inequalities and a strong law of large numbers for END random variables under sub-linear expectations

Abstract

The focus of our work is to investigate exponential inequalities for extended negatively dependent (END) random variables in sub-linear expectations. Through these exponential inequalities, we were able to establish the strong law of large numbers with convergence rate $ O\left(n^{-1/2}\ln^{1/2}n\right) $. Our findings in sub-linear expectation spaces have extended the corresponding results previously established in probability space.

Keywords

• sub-linear expectation
• exponential inequality
• strong law of large numbers
• convergence rate
• end random variables