A variant of importance splitting for rare event estimation

Abstract

Importance splitting is a simulation technique to estimate very small entrance probabilities for Markov processes by splitting sample paths at various stages before reaching the set of interest. This can be done in many ways, yielding different variants of the method. In this context, we propose a new one, called fixed number of successes. We prove unbiasedness for the new and some known variants, because in many papers, the proof is based on an incorrect argument. Further, we analyze its behavior in a simplified setting in terms of efficiency and asymptotics in comparison to the standard variant. The main difference is that it controls the imprecision of the estimator rather than the computational effort. Our analysis and simulation examples show that it is rather robust in terms of parameter choice and we present a two-stage procedure which also yields confidence intervals.