Rare-Event Simulation for the Hitting Time of Gaussian Processes

In reliability theory and network performance analysis a relevant role is played by the time needed to reach a given threshold, known in probability theory as hitting time. Although such issue has been widely investigated, closed-form results are available only for independent increments of the input process. Hence, in this paper we focus on the estimation of the upper tail of the hitting time distribution for general Gaussian processes by means of discrete-event simulation. Indeed, Gaussian processes often arise as a powerful modelling tool in many real-life systems and suitable ad-hoc techniques have developed for their analysis and simulation. Since the event of interest becomes rare as the threshold increases, a variant of Conditional Monte Carlo, based on the bridge process, is introduced and the explicit expression of the estimator is derived. Finally, simulation results highlight the unbiasedness and effectiveness (in terms of relative error) of the proposed approach