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Methodology and Computing in Applied Probability

, Volume 11, Issue 3, pp 279–306 | Cite as

Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables

  • Dominik Kortschak
  • Hansjörg AlbrecherEmail author
Article

Abstract

In this paper 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.

Keywords

Subexponential tail Dependence Copula Multivariate regular variation Maximum domain of attraction 

AMS 2000 Subject Classification

60G70 62E20 62H20 62P05 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Radon InstituteAustrian Academy of SciencesLinzAustria
  2. 2.University of LinzLinzAustria

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