Bridge Monte-Carlo: a novel approach to rare events of Gaussian processes

In this work we describe a new technique, alternative to Importance Sampling (IS), for the Monte-Carlo estimation of rare events of Gaussian processes which we call Bridge Monte-Carlo (BMC). This topic is relevant in teletraffic engineering where queueing systems can be fed by long-range dependent stochastic processes usually modelled through fraction Brownian motion. We show that the proposed approach has clear advantages over the widespread single-twist IS and at the same time has the same computational complexity.