Importance sampling for stochastic simulations
Management Science
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Restart: a straightforward method for fast simulation of rare events
WSC '94 Proceedings of the 26th conference on Winter simulation
Fast simulation of rare events in queueing and reliability models
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On the efficiency of the splitting and roulette approach for sensitivity analysis
Proceedings of the 29th conference on Winter simulation
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
A comparison of RESTART implementations
Proceedings of the 30th conference on Winter simulation
Multilevel Splitting for Estimating Rare Event Probabilities
Operations Research
Variance Reduction via Lattice Rules
Management Science
On the efficiency of RESTART for multidimensional state systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Limit theorems for the multilevel splitting algorithm in the simulation of rare events
WSC '05 Proceedings of the 37th conference on Winter simulation
Rare events, splitting, and quasi-Monte Carlo
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Introduction to Rare Event Simulation
Introduction to Rare Event Simulation
A preliminary study of optimal splitting for rare-event simulation
Proceedings of the 40th Conference on Winter Simulation
Reachability Analysis for Stochastic Hybrid Systems Using Multilevel Splitting
HSCC '09 Proceedings of the 12th International Conference on Hybrid Systems: Computation and Control
Using stochastic petri nets for level-crossing collision risk assessment
IEEE Transactions on Intelligent Transportation Systems
A variant of importance splitting for rare event estimation: Fixed number of successes
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Statistical verification of probabilistic properties with unbounded until
SBMF'10 Proceedings of the 13th Brazilian conference on Formal methods: foundations and applications
Multilevel splitting for reachability analysis of stochastic hybrid systems
Proceedings of the 2010 Conference on Grand Challenges in Modeling & Simulation
Efficient Monte Carlo simulation via the generalized splitting method
Statistics and Computing
Coupling and importance sampling for statistical model checking
TACAS'12 Proceedings of the 18th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Simulating network cyber attacks using splitting techniques
Proceedings of the Winter Simulation Conference
Combining simulation allocation and optimal splitting for rare-event simulation optimization
Proceedings of the Winter Simulation Conference
Static Network Reliability Estimation via Generalized Splitting
INFORMS Journal on Computing
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Splitting and importance sampling are the two primary techniques to make important rare events happen more frequently in a simulation, and obtain an unbiased estimator with much smaller variance than the standard Monte Carlo estimator. Importance sampling has been discussed and studied in several articles presented at the Winter Simulation Conference in the past. A smaller number of WSC articles have examined splitting. In this paper, we review the splitting technique and discuss some of its strengths and limitations from the practical viewpoint. We also introduce improvements in the implementation of the multilevel splitting technique. This is done in a setting where we want to estimate the probability of reaching B before reaching (or returning to) A when starting from a fixed state x0 ∈ B, where A and B are two disjoint subsets of the state space and B is very rarely attained. This problem has several practical applications.