The Estimation Of Rare Event Probability Via Generalized Splitting Techniques

Rare event means that the occurrence probability of the event is very small. Although the rare event is difficult to occur, if it happens, it can cause very serious consequences. Therefore the simulation of the probability of rare event probability has been a concern of the people.The simulation of rare event occurrence probability is a field of stochastic simulation. Important Splitting method is one of the important techniques to improve the speed and accuracy of the rare event simulation. In this paper, based on the traditional Splitting method, proposes a Generalized Splitting(GS) method, which improves the diversity of samples. In theory, it is proved that GS method can be used to get the unbiased estimation of the probability of rare event and the unbiased estimation of the variance, and use the R program to implement the algorithm. According to the idea of GS method, we propose the Effort Generalized Splitting(FE-GS) method. We compare the GS method with the FE-GS method by the theoretical analysis and the verification of the classic example. The conclusion is that the GS method is better than the FE-GS splitting method in the convergence speed and precision.