Tail Behavior of Sums and Maxima of Sums of Dependent Subexponential Random Variables

In this paper, we consider dependent random variables X k , k=1,2,… with supports on [−b k ,∞), respectively, where the b k ≥0 are some finite constants. We derive asymptotic results on the tail probabilities of the quantities $S_{n}=\sum_{k=1}^{n} X_{k}$ , X (n)=max 1≤k≤n X k and S (n)=max 1≤k≤n S k , n≥1 in the case where the random variables are dependent with heavy-tailed (subexponential) distributions, which substantially generalize the results of Ko and Tang (J. Appl. Probab. 45, 85–94, 2008).