On sums of conditionally independent subexponential random variables

Serguei Foss, Andrew Richards

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random variables, for both deterministic and random sums, using a fresh approach, by considering conditional independence structures on the random variables. We seek sufficient conditions for the results of the theory with independent random variables to still hold. For a subexponential distribution, we introduce the concept of a boundary class of functions, which we hope will be a useful tool in studying many aspects of subexponential random variables. The examples we give demonstrate a variety of effects owing to the dependence, and are also interesting in their own right. © 2010 INFORMS.

Original languageEnglish
Pages (from-to)102-119
Number of pages18
JournalMathematics of Operations Research
Volume35
Issue number1
DOIs
Publication statusPublished - Feb 2010

Keywords

  • Conditional independence
  • Heavy tails
  • Subexponentiality

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