The Estimation Of Rare Event Probabilities Via Splitting Techniques

The occurrence probability of the rare event is extremely small. If the rare event happens, it can cause very serious consequences, such as earthquake and the financial crisis. Therefore the simulation of the occurrence probability of rare event is probably one of the most popular topics recently.In the simulation of rare event, it may take large sample sizes to get the estimator of the rare event. Sometimes it can lead to a variance explosion and increase the computing time. In this paper, we study the splitting techniques which accelerate the rate of occurrence of the rare events to solve the problem. We first introduce what is rare event,the importance of studying rare events and the background of the splitting techniques.Then we introduce the mathematical principle and algorithms of the splitting techniques.After that, we use the splitting techniques to simulate the rare events under some important cases of light tail and heavy tail. Finally, we get the conclusion of this paper which combined the results of examples.