Resumen de On a new concept of stochastic domination and the laws of large numbers

Lé Ván Thiêm

• Consider a sequence of positive integers {kn,n≥1}, and an array of nonnegative real numbers {an,i,1≤i≤kn,n≥1} satisfying supn≥1∑kni=1an,i=C0∈(0,∞). This paper introduces the concept of {an,i}-stochastic domination. We develop some techniques concerning this concept and apply them to remove an assumption in a strong law of large numbers of Chandra and Ghosal (Acta Math Hung 71(4):327–336, 1996). As a by-product, a considerable extension of a recent result of Boukhari (J Theor Probab, 2021. https://doi.org/10.1007/s10959-021-01120-6) is established and proved by a different method. The results on laws of large numbers are new even when the summands are independent. Relationships between the concept of {an,i}-stochastic domination and the concept of {an,i}-uniform integrability are presented. Two open problems are also discussed.