- On max-sum equivalance and convolution closure of heavy-tailed distributions and their applications
- Journal of Applied Probability
- Volume | Issue number
- 41 | 1
- Pages (from-to)
- Number of pages
- Document type
- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
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.
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