On sums of conditionally independent subexponential random variables

On sums of conditionally independent subexponential random variables

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Article ID: iaor20102611
Volume: 35
Issue: 1
Start Page Number: 102
End Page Number: 119
Publication Date: Feb 2010
Journal: Mathematics of Operations Research
Authors: ,
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.

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