In this paper we establish weak convergence theorems for weighted empirical processes of strong mixing, $\rho$-mixing and associated sequences. We apply these results to obtain weak convergence of integral functionals of empirical processes and of mean residual life processes in reliability theory. To carry out the proofs, we develop two Rosenthal-type inequalities for strong mixing and associated sequences.
"Weak convergence for weighted empirical processes of dependent sequences." Ann. Probab. 24 (4) 2098 - 2127, October 1996. https://doi.org/10.1214/aop/1041903220