Asymptotic results for the sum of dependent non-identically distributed random variables. (English) Zbl 1171.60348
Summary: We extend some results about the probability that the sum of \(n\) dependent subexponential random variables exceeds a given threshold \(u\). In particular, the case of non-identically distributed and not necessarily positive random variables is investigated. Furthermore we establish criteria how far the tail of the marginal distribution of an individual summand may deviate from the others so that it still influences the asymptotic behavior of the sum. Finally we explicitly construct a dependence structure for which, even for regularly varying marginal distributions, no asymptotic limit of the tail of the sum exists. Some explicit calculations for diagonal copulas and \(t\)-copulas are given.
MSC:
| 60G70 | Extreme value theory; extremal stochastic processes |
| 60E05 | Probability distributions: general theory |
| 91B30 | Risk theory, insurance (MSC2010) |
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