Random Sums of Random Variables and Vectors

Edward Omey () and R Vesilo ()
Additional contact information
Edward Omey: Hogeschool-Universiteit Brussel (HUB), Belgium
R Vesilo: Macquarie University, Sydney, Australia

No 2009/09, Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management

Abstract: Let fX;Xi; i = 1; 2; :::g denote independent positive random variables having a common distribution function F(x) and, independent of X, let N denote an integer valued random variable. Using S(0) = 0 and S(n) = S(n ?? 1) + Xn, the random sum S(N) has distribution function G(x) = 1Xi=0 P(N = i)P(S(i) _ x) and tail distribution G(x) = 1 ?? G(x). In which case, we say that the distribution function G is subordinated to F with subordinator N. Under suitable conditions, it can be proved that G(x) s E(N)F(x) as x ! 1. In this paper, we extend some of the existing results. In the place of i.i.d. random variables, we use variables that are independent or variables that are asymptotically in- dependent. We also consider multivariate subordinated distribution functions.

Keywords: Subexponential distributions; regular variation; O-regular variation; subordination (search for similar items in EconPapers)
Pages: 31 pages
Date: 2009-05-15
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://lirias.hubrussel.be/bitstream/123456789/2469/1/09HRP09.pdf (application/pdf)
Our link check indicates that this URL is bad, the error code is: 500 Can't connect to lirias.hubrussel.be:443 (nodename nor servname provided, or not known)

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:hub:wpecon:200909

Access Statistics for this paper

More papers in Working Papers from Hogeschool-Universiteit Brussel, Faculteit Economie en Management Contact information at EDIRC.
Bibliographic data for series maintained by Sabine Janssens ( this e-mail address is bad, please contact ).