Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
The asymptotic efficiency of simulation estimators
Operations Research
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for Markov chains: computing variance and determining optimal measures
WSC '96 Proceedings of the 28th conference on Winter simulation
Generalized zero-variance solutions and intelligent random numbers
WSC '87 Proceedings of the 19th conference on Winter simulation
Proceedings of the 33nd conference on Winter simulation
Approximating Martingales for Variance Reduction in Markov Process Simulation
Mathematics of Operations Research
Journal of Complexity
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Variance Reduction via Lattice Rules
Management Science
Journal of Complexity
Combination of General Antithetic Transformations and Control Variables
Mathematics of Operations Research
Good Lattice Rules in Weighted Korobov Spaces with General Weights
Numerische Mathematik
Function-approximation-based importance sampling for pricing American options
WSC '04 Proceedings of the 36th conference on Winter simulation
Estimating the probability of a rare event over a finite time horizon
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Non-linear control variates for regenerative steady-state simulation
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
Adaptive Control Variates for Finite-Horizon Simulation
Mathematics of Operations Research
A Randomized Quasi-Monte Carlo Simulation Method for Markov Chains
Operations Research
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Efficient importance sampling under partial information
Proceedings of the Winter Simulation Conference
Markov chain importance sampling with applications to rare event probability estimation
Statistics and Computing
An importance sampling method based on a one-step look-ahead density from a Markov chain
Proceedings of the Winter Simulation Conference
Proceedings of the Winter Simulation Conference
Static Network Reliability Estimation via Generalized Splitting
INFORMS Journal on Computing
Zero-Variance Importance Sampling Estimators for Markov Process Expectations
Mathematics of Operations Research
Computers and Operations Research
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Monte Carlo simulation applies to a wide range of estimation problems, but converges rather slowly in general. Variance reduction techniques can lower the estimation error, sometimes by a large factor, but rarely change the convergence rate of the estimation error. This error usually decreases as the inverse square root of the computational effort, as dictated by the central limit theorem. In theory, there exist simulation estimators with zero variance, i.e., that always provide the exact value. The catch is that these estimators are usually much too difficult (or virtually impossible) to implement. However, there are situations, especially in the context of rare-event simulation, where the zero-variance simulation can be approximated well enough to provide huge efficiency gains. Adaptive versions can even yield a faster convergence rate, including exponential convergence in some cases. This paper gives a brief overview of these methods and discuss their practicality.