A MEAN CONVERGENCE THEOREM FOR TRIANGULAR ARRAYS OF ROWWISE AND PAIRWISE mn-DEPENDENT RANDOM VARIABLES

Abstract

This paper establishes a mean convergence theorem for triangular arrays of rowwise and pairwise mn-dependent random variables. Some authors studied limit theorems for sequences of pairwise m-dependent random variables where m is fixed (see, e.g., Quang and Nguyen [Applications of Mathematics, 2016] and Thanh [Bulletin of the Institute of Mathematics Academia Sinica, 2005]). In this paper, we establish a limit theorem for triangular arrays of rowwise and pairwise mn-dependent random variables, where mn may approach infinity as n → ∞. The main theorem extends some results in the literature, including Theorem 3.1 of Chen, Bai and Sung in [Journal of Mathematical Analysis and Applications, 2014].

Keywords

• convergence in mean
• pairwise mn-dependence
• uniform integrability in the cesàro sense
• triangular array of random variables