A dynamic importance sampling method for quick simulation of rare events

Simulation of low-probability events may take extremely long times since they occur very rarely. There are various variance reduction methods used to speed up simulations in such cases. In this thesis, a new variance reduction technique is proposed, which is based on expressing the desired probability as the product of a number of greater probabilities and estimating each term in the product in a recursive manner. It turns out that the resulting estimator, when feasible, uses an importance sampling distribution at each step to constrain the samples into a sequence of larger sets which shrink towards the rare set gradually. Moreover, the important samples used in each step are obtained automatically from the outcomes of the experiments in the previous steps. The method is applied to the estimation of overflow probability in a network of queues and remarkable speed-ups with respect to standard simulation are obtained.