Subexponential asymptotics of hybrid fluid and ruin models
  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. 
Bert Zwart, Sem Borst and Krzystof Debicki