An importance sampling method 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 in this paper, in which the classical exponential change of measure is adopted to construct the family of importance sampling distributions, and the optimal importance sampling distribution is obtained by minimizing the variance of importance sampling estimator. Numerical experiment has been conducted and the result indicates that the method can effectively estimate the rare event probability.