This paper shows how the modern machinery for generating abstract empirical central limit theorems can be applied to arrays of dependent variables. It develops a bracketing approximation based on a moment inequality for sums of strong mixing arrays, in an eﬀort to illustrate the sorts of diﬀiculty that need to be overcome when adapting the empirical process theory for independent variables. Some suggestions for further development are oﬀered. The paper is largely self-contained.
Andrews, Donald W.K. and Pollard, David, "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes" (1990). Cowles Foundation Discussion Papers. 1194.