Open Access
February 2005 Subexponential asymptotics of hybrid fluid and ruin models
Bert Zwart, Sem Borst, Krzystof Dȩbicki
Ann. Appl. Probab. 15(1A): 500-517 (February 2005). DOI: 10.1214/105051604000000648


We ķ investigate the tail asymptotics of the supremum of X(t)+Y(t)−ct, where X={X(t),t≥0} and Y={Y(t),t≥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.


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Bert Zwart. Sem Borst. Krzystof Dȩbicki. "Subexponential asymptotics of hybrid fluid and ruin models." Ann. Appl. Probab. 15 (1A) 500 - 517, February 2005.


Published: February 2005
First available in Project Euclid: 28 January 2005

zbMATH: 1079.60037
MathSciNet: MR2115050
Digital Object Identifier: 10.1214/105051604000000648

Primary: 60G15
Secondary: 60F10 , 60G70

Keywords: Extremes , fractional Brownian motion , Gaussian processes , On-Off processes , perturbed risk models , regular variation , ruin probabilities , Subexponential distributions

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.15 • No. 1A • February 2005
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