Associated sequences have been studied extensively in recent years. Burton et al. (1986) introduced a generalization of association to d-dimensional random vectors and proved Functional Central Limit Theorems. In the present paper a Berry-Esséen theorem and a Functional Law of the Iterated...

We present a new technique for proving the empirical process invariance principle for stationary processes (Xn)n=0. The main novelty of our approach lies in the fact that we only require the central limit theorem and a moment bound for a restricted class of functions (f(Xn))n=0, not containing...

We establish a multivariate empirical process central limit theorem for stationary -valued stochastic processes (Xi)i=1 under very weak conditions concerning the dependence structure of the process. As an application, we can prove the empirical process CLT for ergodic torus automorphisms. Our...

The positive dependence notion of association for collections of random variables is generalized to that of weak association for collections of vector valued random elements in such a way as to allow negative dependencies in individual random elements. An invariance principle is stated and...