In this paper we consider conditionally independent processes with respect to some dynamic factor. We derive some mixing properties for random processes when conditioning is given with respect to unbounded memory of the factor. Our work is motivated by some real examples related to risk theory.

Conditional dependence is expressed as a projection map in the trivariate copula space. The projected copula, its sample counterpart and the related process are defined. The weak convergence of the projected copula process to a tight centered Gaussian Process is obtained under weak assumptions...