Limit theorems for empirical processes based on dependent data

Let (X-n) be any sequence of random variables adapted to a filtration (G(n)). Define a(n)(.) = P(Xn+1 is an element of . vertical bar G(n)), b(n) = 1/n Sigma(n-1)(i=0) a(i), and mu(n) = 1/n Sigma(n)(i=1) delta(Xi). Convergence in distribution of the empirical processes B-n = root n (mu(n) - b(n)) and C-n = root n (mu(n) - a(n)) 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.