A note on weighted infinite sums of dependent regularly varying tailed random variables

In this paper we study the asymptotic tail behavior of weighted infinite sums of heavy-tailed random variables under a general dependence structure. Our result shows that the regular variation at tails does not only eliminate the given dependence structure, but the aggregate tail probabilities are asymptotically determined by the sums of the individual tail probabilities with positive coefficients. The result will be illustrated with examples.