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| Asymptotic Results for Tail Probabilities of Sums of Dependent and Heavy-Tailed Random Variables |
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Citation： |
Kam Chuen YUEN,Chuancun YIN.Asymptotic Results for Tail Probabilities of Sums of Dependent and Heavy-Tailed Random Variables[J].Chinese Annals of Mathematics B,2012,33(4):557~568 |
| Page view： 1771
Net amount： 1284 |
Authors： |
Kam Chuen YUEN; Chuancun YIN; |
Foundation： |
the National Natural Science Foundation of China (No. 11171179), the Research Fund for the Doctoral Program of Higher Education of China (No. 20093705110002). |
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| Abstract： |
Let $X_1, X_2, \cdots $ be a sequence of dependent and heavy-tailed random variables with distributions $F_1, F_2,\cdots$ 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, the asymptotic behavior of the tail probabilities of the quantities $S_n =\sum\limits_{k=1}^n X_k$ and $S_{(n)}=\max\limits_{1\le k\le n} S_k$ for $n>1$, and their randomized versions $S_{\tau}$ and $S_{(\tau)}$ are studied. Some applications to the risk theory are presented. |
Keywords： |
Asymptotic tail probability, Copula, Heavy-tailed distribution, Partial sum, Risk process |
Classification： |
62E20, 91B30, 62P05 |
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