IEEE/ACM Transactions on Networking (TON)
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Heavy-tailed probability distributions in the World Wide Web
A practical guide to heavy tails
Simulating heavy tailed processes using delayed hazard rate twisting
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling simulation in the presence of heavy tails
WSC '05 Proceedings of the 37th conference on Winter simulation
Efficient tail estimation for sums of correlated lognormals
Proceedings of the 40th Conference on Winter Simulation
Efficient rare event simulation for heavy-tailed compound sums
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On importance sampling with mixtures for random walks with heavy tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Small Variance Estimators for Rare Event Probabilities
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special Issue on Monte Carlo Methods in Statistics
On error rates in rare event simulation with heavy tails
Proceedings of the Winter Simulation Conference
Markov chain importance sampling with applications to rare event probability estimation
Statistics and Computing
Rare event simulation techniques
Proceedings of the Winter Simulation Conference
Efficient rare event simulation for heavy-tailed systems via cross entropy
Proceedings of the Winter Simulation Conference
Importance sampling for stochastic recurrence equations with heavy tailed increments
Proceedings of the Winter Simulation Conference
Rare-event simulation for stochastic recurrence equations with heavy-tailed innovations
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient simulations for the exponential integrals of Hölder continuous gaussian random fields
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. For random variables with heavy tails there is little consensus on how to choose the change of measure used in importance sampling. In this article we study dynamic importance sampling schemes for sums of independent and identically distributed random variables with regularly varying tails. The number of summands can be random but must be independent of the summands. For estimating the probability that the sum exceeds a given threshold, we explicitly identify a class of dynamic importance sampling algorithms with bounded relative errors. In fact, these schemes are nearly asymptotically optimal in the sense that the second moment of the corresponding importance sampling estimator can be made as close as desired to the minimal possible value.