Simulation in exponential families
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for sums of random variables with regularly varying tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
Efficient Monte Carlo simulation via the generalized splitting method
Statistics and Computing
On large deviations theory and asymptotically efficient Monte Carlo estimation
IEEE Transactions on Information Theory
Fitting mixture importance sampling distributions via improved cross-entropy
Proceedings of the Winter Simulation Conference
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Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events defined through large exceedances of the empirical mean of summands of a random walk, in the domain of large or moderate deviations. The approximation of conditional density of the trajectory of the random walk is handled on long runs. The length of those runs which is compatible with a given accuracy is discussed; simulated results are presented, which enlight the gain of the present approach over classical Importance Sampling schemes. Detailed algorithms are proposed.