Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Tail Asymptotics for the Supremum of a Random Walk when the Mean Is not Finite
Queueing Systems: Theory and Applications
Efficient simulations for the exponential integrals of Hölder continuous gaussian random fields
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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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.