SOME RESULTS ON THE CONCEPT OF {𝑎𝑚,𝑛,𝑖,𝑗 } – STOCHASTIC DOMINATION FOR DOUBLE ARRAYS OF RANDOM VARIABLES

In this paper, we prove some results on the concept of {𝑎𝑚,𝑛,𝑖,𝑗}- stochastic domination for double arrays of random variables, where {𝑘𝑚, 𝑚 ≥ 1} and {𝑙𝑛, 𝑛 ≥ 1 } are two sequences of positive integers and {𝑎𝑚,𝑛,𝑖,𝑗; 1 ≤ 𝑖 ≤ 𝑘𝑚, 1 ≤ 𝑗 ≤ 𝑙𝑛, 𝑚, 𝑛 ≥ 1} is sequences of positive constants satisfying sup 𝑚≥1,𝑛≥1 ∑ ∑ 𝑎𝑚,𝑛,𝑖,𝑗 = 𝐶0, 𝐶0 ∈ (0, ∞). 𝑙𝑛 𝑗=1 𝑘𝑚 𝑖=1 The main results establish double sum versions of Theorem 2.1 and Theorem 2.6 of Thành (2023). Keywords: Stochastic domination; double array; slowly varying function; Cesàro stochastic domination