Subexponential asymptotics of hybrid fluid and ruin models

Details Subexponential asymptotics of hybrid fluid and ruin models Subexponential asymptotics of hybrid fluid and ruin models

2005-03-23

arxiv.org/abs/math/0503482v1

Annals of Applied Probability 2005, Vol. 15, No. 1A, 500-517

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000648 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000648

We 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.

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