Bivariate CDF iterations and asymptotic independence (Q1092568)

The authors study bivariate cdf iterands and asymptotic independence under weak convergence of sequences of bivariate random vectors via the behavior of a certain class of bivariate cdf iterands that includes the extreme value iterand and a certain maximin iterand. Two types of cdf iterands are treated. At first, they deal with bivariate iterands whose marginal iterands have no ``interior'' fixed points. And then they treat bivariate iterands whose marginal iterands have a unique interior fixed point. The main results provide necessary and sufficient conditions for asymptotic independence. Specializations to extreme value iteration and maximin iteration are also included.