Subexponential asymptotics of hybrid fluid and ruin models

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dc.creatorZwart, Bert
dc.creatorBorst, Sem
dc.creatorDebicki, Krzystof
dc.date2005-03-23
dc.date.accessioned2026-07-07T05:18:15Z
dc.date.available2026-07-07T05:18:15Z
dc.descriptionWe investigate the tail asymptotics of the supremum of X(t)+Y(t)-ct, where X={X(t),t\geq 0} and Y={Y(t),t\geq 0} are two independent stochastic processes. We assume that the process Y has subexponential characteristics and that the process X is more regular in a certain sense than Y. A key issue examined in earlier studies is under what conditions the process X contributes to large values of the supremum only through its average behavior. The present paper studies various scenarios where the latter is not the case, and the process X shows some form of ``atypical'' behavior as well. In particular, we consider a fluid model fed by a Gaussian process X and an (integrated) On-Off process Y. We show that, depending on the model parameters, the Gaussian process may contribute to the tail asymptotics by its moderate deviations, large deviations, or oscillatory behavior.
dc.descriptionPublished at http://dx.doi.org/10.1214/105051604000000648 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0503482
dc.identifierhttp://arxiv.org/abs/math/0503482
dc.identifierAnnals of Applied Probability 2005, Vol. 15, No. 1A, 500-517
dc.identifierdoi:10.1214/105051604000000648
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74599
dc.subjectProbability
dc.subject60G15 (Primary) 60F10, 60G70. (Secondary)
dc.titleSubexponential asymptotics of hybrid fluid and ruin models
dc.typetext

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