Uniform Approximation for the Tail Behavior of Bidimensional Randomly Weighted Sums

The uniform approximation for the tail behavior of bidimensional randomly weighted sums is considered in this paper. The primary random vectors are supposed to have extended regularly varying tails, while the underlying dependence between the components is described by some quasi-extended-regular-variation (QERV) copula functions. There are mild moment conditions on the random weight vectors without any assumptions on the dependence structures between themselves. The case when the number of the sums is extended to an integer-valued random variable is investigated additionally. A direct application of the results in a stochastic difference equation and some numerical simulations are also stated.