Asymptotic tail behavior of a random sum with conditionally dependent subexponential summands

Abstract

In this paper, we obtain some results for the asymptotic behavior of the tail probability of a random sum Sτ = ∑τk = 1Xk, where the summands Xk, k = 1, 2, …, are conditionally dependent random variables with a common subexponential distribution F, and the random number τ is a non negative integer-valued random variable, independent of {Xk: k ⩾ 1}.