On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications
On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications
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DOI：
10.1239/jap/1077134672
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发表时间：
2004-03
影响因子：
1
通讯作者：
Jun Cai;Q. Tang
中科院分区：
文献类型：
--
作者：
Jun Cai;Q. Tang
本文讨论了重尾分布的最大和等价与卷积闭包。我们推广了著名的最大和等价和卷积封闭类的正规变化到两个更大的类的重尾分布。作为这些结果的应用，我们研究了复合几何卷积尾的渐近性态，α-稳定Lévy运动扰动下复合Poisson风险过程的破产概率，以及M/G/k排队的平衡等待时间分布.
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 α-stable Lévy motion, and the equilibrium waiting-time distribution of the M/G/k queue.