A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers

Abstract

In this correspondence, we present new results concerning the concept of stochastic domination and apply them to obtain new results on uniform integrability and on the strong law of large numbers for sequences of pairwise independent random variables. Our result on the strong law of large numbers extends a result of Chen, Bai, and Sung (2014). The sharpness of the results is illustrated by three examples.