In this paper, we investigate asymptotic properties of the tail probabilities of the maxima of partial sums of independent random variables. For some large classes of heavy-tailed distributions, we show that the tail probabilities of the maxima of the partial sums asymptotically equal to the sum of the tail probabilities of the individual random variables. Then we partially extend the result to...

Tail conditional expectations refer to the expected values of random variables conditioning on some tail events and are closely related to various coherent risk measures. In the univariate case, the tail conditional expectation is asymptotically proportional to the value-at-risk, a popular risk measure. The focus of this paper is on asymptotic relations between the multivariate tail conditional...

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upper order statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called “semiheavy” tailed distributions. The estimation method is demonstrated on s...

Asymptotics for the number of descendants in the supercritical Galton–Watson process: heavy-tailed case Abstract As well known, for a supercritical Galton–Watson process Z n whose offspring distribution has mean m > 1, the ratio W n := Z n /m n has a.s. limit, say W. We study tail behaviour of the distributions of W n and W in the case where Z 1 has heavy-tailed distribution, that is, Ee λZ1 = ...

From a rare events perspective, scheduling disciplines that work well under light (exponential) tailed workload distributions do not perform well under heavy (power) tailed workload distributions, and vice-versa, leading to fundamental problems in designing schedulers that are robust to distributional assumptions on the job sizes. This paper shows how to exploit partial workload information (sy...

In present teletraac applications of queueing theory service time distributions B(t) with a heavy tail occur, i.e. 1 ? B(t) t ? for t ! 1 with > 1. For such service time distributions not much explicit information is available concerning the tail probabilities of the inherent waiting time distribution W (t). In the present study the waiting time distribution is studied for a stable M=G=1 model ...

AMS 2000 subject classifications: 62H20 62P05 Keywords: Tail dependence Heavy tails Copula Multivariate extreme value distribution Marshall–Olkin distribution Archimedean copula Contagion risk a b s t r a c t The orthant tail dependence describes the relative deviation of upper-(or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its c...