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

Methodology and Computing in Applied Probability volume 11, pages 279–306 (2009)Cite this 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.

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Authors and Affiliations

  1. Radon Institute, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria

    Dominik Kortschak & Hansjörg Albrecher

  2. University of Linz, Altenbergerstrasse 69, 4040, Linz, Austria

    Hansjörg Albrecher

Authors
  1. Dominik Kortschak
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  2. Hansjörg Albrecher
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Corresponding author

Correspondence to Hansjörg Albrecher.

Additional information

Dominik Kortschak was supported by the Austrian Science Fund Project P18392.

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Kortschak, D., Albrecher, H. Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables. Methodol Comput Appl Probab 11, 279–306 (2009). https://doi.org/10.1007/s11009-007-9053-3

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  • DOI: https://doi.org/10.1007/s11009-007-9053-3

Keywords

  • Subexponential tail
  • Dependence
  • Copula
  • Multivariate regular variation
  • Maximum domain of attraction

AMS 2000 Subject Classification

  • 60G70
  • 62E20
  • 62H20
  • 62P05