Weak max-sum equivalence for dependent heavy-tailed random variables

We consider real-valued random variables X 1 ,…, X n with corresponding distributions F 1 ,…, F n such that X 1 ,…, X n admit some dependence structure and n −1 ( F 1 +· · ·+ F n ) belongs to the class of dominatedly varyingtailed distributions. We establish weak equivalence relations among P ( S n > x ), P (max{ X 1 ,…, X n } > x ), P (max{ S 1 ,…, S n } > x ), and ∑ k = 1 n F k ¯ x as x → ∞, where S k := X 1 + · · · + X k . Some copula-based examples illustrate the results.