Strong approximation of empirical copula process by Kiefer process

This paper investigates the problem of strong approximation of the empirical copula process for arbitrary dimension, with continuous unknown margins. The idea of the proof is based on an original idea exposed by Deheuvels et al. (2006), and the theorem of strong approximation for an arbitrary distribution function proved in Cs\"orgo and Horv\'ath (1988). Using these results, we derive the normality for smoothed empirical copula process and L.I.L. for empirical process of copulas.