Weak convergence in Lp(0,1) of the uniform empirical process under dependence

Abstract

The weak convergence of the empirical process of strong mixing or associated random variables is studied in LP(0,1). We find minimal rates of convergence to zero of the mixing coefficients or the covariances, in either case, supposing stationarity of the underlying variables. The rates obtained improve, for p not too large, the corresponding results in the classical D(0,1) framework.