On max-sum equivalance and convolution closure of heavy-tailed distributions and their applications
| Authors |
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| Publication date | 2004 |
| Journal | Journal of Applied Probability |
| Volume | Issue number | 41 | 1 |
| Pages (from-to) | 117-130 |
| Number of pages | 14 |
| Organisations |
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| Abstract | In this paper, we discuss max-sum equivalence and convolution closure of heavy-tailed distributions. We generalize the well-known max-sum equivalence and convolution closure in the class of regular variation to two larger classes of heavy-tailed distributions. As applications of these results, we study asymptotic behaviour of the tails of compound geometric convolutions, the ruin probability in the compound Poisson risk process perturbed by an ¿-stable Lévy motion, and the equilibrium waiting-time distribution of the M/G/k queue. |
| Document type | Article |
| Published at |
https://doi.org/10.1239/jap/1077134672
(Final published version)
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