# A Strong Invariance Theorem of the Tail Empirical Copula Processes

Published in *Communications in Statistics - Theory and Methods*, 2013

### S. Bouzebda and T. Zari

We study the behavior of bivariate empirical copula process \(\mathbb{G}_n(\cdot,\cdot)\) on pavements \([0,k_n/n]^2\) of \([0,1]^2,\) where \(k_n\) is a sequence of positive constants fulfilling some conditions. We provide a upper bound for the strong approximation of \(\mathbb{G}_n(\cdot,\cdot)\) by a Gaussian process when \(k_n/n \searrow \gamma\) as \(n\rightarrow \infty,\) where \(0 \leq \gamma \leq 1.\)