On Efficiency of Multilevel Splitting

This article focuses on estimating rare events using multilevel splitting schemes. The event of interest is that a Markov process enters some rare set before another (“tabu”) set. It is known that in this setting a large deviations analysis is not always sufficient for constructing asymptotically efficient importance sampling schemes; additional modifications to the change of measure suggested by large deviations are needed. As an alternative, we design an asymptotically efficient multilevel splitting scheme that relies on the large deviations analysis only. This property makes it more flexible and easier to implement than corresponding importance sampling schemes.