An importance sampling method based on martingale with applications to rare event probability

It usually takes long time to simulate rare event using traditional Monte Carlo method, while importance sampling techniques can effectively reduce the simulation time and improve simulation efficiency. A new implementation for importance sampling method to estimate rare event probability in simulation models is proposed. The optimal importance sampling distributions was obtained by making use of the martingale constructed by likelihood ratio. The computation results were compared with the importance sampling based on cross-entropy, the importance sampling based on minimizing variance and crude Monte Carlo method. Numerical experiments had been conducted and the results indicate that the method can effectively estimate the rare event probabilities.