Rare-event simulation for a multidimensional random walk with t distributed increments
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Importance sampling for Jackson networks
Queueing Systems: Theory and Applications
A general framework of importance sampling for value-at-risk and conditional value-at-risk
Winter Simulation Conference
Operations Research Letters
Efficient importance sampling under partial information
Proceedings of the Winter Simulation Conference
Efficient estimation of density and probability of large deviations of sum of IID random variables
Proceedings of the Winter Simulation Conference
| Hi-index | 0.00 |
Successful efficient rare-event simulation typically involves using importance sampling tailored to a specific rare event. However, in applications one may be interested in simultaneous estimation of many probabilities or even an entire distribution. In this paper, we address this issue in a simple but fundamental setting. Specifically, we consider the problem of efficient estimation of the probabilities P(Sn ≥ na) for large n, for all a lying in an interval A, where Sn denotes the sum of n independent, identically distributed light-tailed random variables. Importance sampling based on exponential twisting is known to produce asymptotically efficient estimates when A reduces to a single point. We show, however, that this procedure fails to be asymptotically efficient throughout A when A contains more than one point. We analyze the best performance that can be achieved using a discrete mixture of exponentially twisted distributions, and then present a method using a continuous mixture. We show that a continuous mixture of exponentially twisted probabilities and a discrete mixture with a sufficiently large number of components produce asymptotically efficient estimates for all a ∈ A simultaneously.