General Central Limit Theorems for m-Dependent Random Variables Under Sub-linear Expectations

M-dependence is a commonly used assumption in the study of dependent sequences. In this paper, central limit theorems for m-dependent random variables under the sub-linear expectations are established based mainly on the conditions of Zhang (Commun Math Stat, 2023). They can be regarded as the extension of independent Lindeberg central limit theorem, and for proving this, Rosenthal’s inequality for m-dependent random variables is obtained. In particular, we extend the results in Li (Acta Math Appl Sin Engl Ser 31:435–444, 2015) and establish the central limit theorem for m-dependent stationary sequence.