Importance splitting for finite-time rare event simulation

In this note, a general framework is proposed for using importance splitting to estimate rare event probabilities with finite-time constraints. We prove that the splitting estimator is unbiased and characterize the optimal splitting curves. A new unbiased estimator with truncated sample paths is proposed to improve computational efficiency, and a pilot algorithm is provided to determine the optimal truncation and splitting curves. Numerical examples illustrate the optimality of the splitting curves and the effectiveness of the new estimator.