Asymptotic results for tail probabilities of sums of dependent heavy-tailed random variables

Abstract

Let $\{X_1,X_2,...\}$ be a sequence of dependent heavy-tailed random variables with distributions $F_1,F_2,...$ on $(-\infty ,\infty )$, and let $\tau$ be a nonnegative integer-valued random variable independent of the sequence $\{X_k,k\ge 1\}$. In this framework, we study the asymptotic behavior of the tail probabilities of the quantities $X_{(n)}={\max }_{1\le k\le n}{X}_k$, $S_n={\sum }_{k=1}^n{X}_k$ and $S_{(n)}={\max }_{1\le k\le n}{S}_k$ for $n>1$, and for those of their randomized versions $X_{(\tau )}$, $S_{\tau }$ and $S_{(\tau )}$. We also consider applications of the results obtained to some commonly-used risk processes.

References in corpus (1)

• On lower limits and equivalences for distribution tails of randomly stopped sums

Cited by in corpus (2)

• Tail behavior of sums and differences of log-normal random variables
• Tails of weakly dependent random vectors