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

Dominik Kortschak () and Hansjörg Albrecher ()
Additional contact information
Dominik Kortschak: Austrian Academy of Sciences
Hansjörg Albrecher: Austrian Academy of Sciences

Methodology and Computing in Applied Probability, 2009, vol. 11, issue 3, 279-306

Abstract: 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; 60G70; 62E20; 62H20; 62P05 (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

Downloads: (external link)
http://link.springer.com/10.1007/s11009-007-9053-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:metcap:v:11:y:2009:i:3:d:10.1007_s11009-007-9053-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-007-9053-3

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().