Limit theorems for empirical processes based on dependent data

Abstract

Let (X n) be any sequence of random variables adapted to a filtration (G n). Define Convergence in distribution of the empirical processes is investigated under uniform distance. If (X n) is conditionally identically distributed, convergence of B n and C n is studied according to Meyer-Zheng as well. Some CLTs, both uniform and non uniform, are proved. In addition, various examples and a characterization of conditionally identically distributed sequences are given.