An Extension of Central Limit Theorem for Randomly Indexed m-Dependent Random Variables

Abstract

In this note, we prove the conjecture in the paper [Shang Y. \emph{A central limit theorem for randomly indexed m-dependent random variables.} Filomat 26.4 (2012): 713-717] about the sum of a random number $N_n$ of $m$-dependent random variables. The random number $N_n$ is supposed to converge in probability toward a positive random variable.