On tail behavior of randomly weighted sums of dependent subexponential random variables

Abstract

In this paper, we revisit the tail behavior of randomly weighted sums and their maxima of dependent subexponential random variables, in which the primary random variables X 1 , … , X n are real-valued and dependent following two general dependence structures, respectively, and the random weights θ 1 , … , θ n are another n positive and arbitrarily dependent random variables, but independent of X 1 , … , X n . . Under some technical conditions, we derive some asymptotic formulas for the tail probability of the randomly weighted sums and their maxima, which coincide with some existing ones in the literature. The merit of our results is that unbounded supports for the random weights are allowed and the distributions of primary random variables can be different.