  The empirical copula process plays a central role in the asymptotic analysis
of many statistical procedures which are based on copulas or ranks. Among other
applications, results regarding its weak convergence can be used to develop
asymptotic theory for estimators of dependence measures or copula densities,
they allow to derive tests for stochastic independence or specific copula
structures, or they may serve as a fundamental tool for the analysis of
multivariate rank statistics. In the present paper, we establish weak
convergence of the empirical copula process (for observations that are allowed
to be serially dependent) with respect to weighted supremum distances. The
usefulness of our results is illustrated by applications to general bivariate
rank statistics and to estimation procedures for the Pickands dependence
function arising in multivariate extreme-value theory.
