Splitting for Rare-Event Simulation

Splitting and importance sampling are the two primary techniques to make important rare events happen more frequently in a simulation, and obtain an unbiased estimator with much smaller variance than the standard Monte Carlo estimator. Importance sampling has been discussed and studied in several articles presented at the winter simulation conference in the past. A smaller number of WSC articles have examined splitting. In this paper, we review the splitting technique and discuss some of its strengths and limitations from the practical viewpoint. We also introduce improvements in the implementation of the multilevel splitting technique. This is done in a setting where we want to estimate the probability of reaching B before reaching (or returning to) A when starting from a fixed state x_o notin B where A and B are two disjoint subsets of the state space and B is very rarely attained. This problem has several practical applications