Splitting algorithms for rare event simulation over long time intervals

In this paper we study the performance of splitting algorithms, and in particular the RESTART method, for the numerical approximation of the probability that a process leaves a neighborhood of a metastable point during some long time interval [0, T ]. We show that, in contrast to alternatives such as importance sampling, the decay rate of the second moment does not degrade as T → ∞. In the course of the analysis we develop some related large deviation estimates that apply when the time interval of interest depends on the large deviation parameter.