Importance sampling for stochastic simulations
Management Science
Importance sampling for the simulation of highly reliable Markovian systems
Management Science
Fast transient simulation of Markovian models of highly dependable systems
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Optimal importance sampling for Markovian systems with applications to tandem queues
Mathematics and Computers in Simulation - Special issue: papers presented at the MSSA/IMACS 11th biennial conference on modelling and simulation
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Generalized zero-variance solutions and intelligent random numbers
WSC '87 Proceedings of the 19th conference on Winter simulation
Probability in the Engineering and Informational Sciences
Function-approximation-based importance sampling for pricing American options
WSC '04 Proceedings of the 36th conference on Winter simulation
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
Rare event simulation for highly dependable systems with fast repairs
Performance Evaluation
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We study an approximation for the zero-variance change of measure to estimate the probability of a rare event in a continuous-time Markov chain. The rare event occurs when the chain reaches a given set of states before some fixed time limit. The jump rates of the chain are expressed as functions of a rarity parameter in a way that the probability of the rare event goes to zero when the rarity parameter goes to zero, and the behavior of our estimators is studied in this asymptotic regime. After giving a general expression for the zero-variance change of measure in this situation, we develop an approximation of it via a power series and show that this approximation provides a bounded relative error when the rarity parameter goes to zero. We illustrate the performance of our approximation on small numerical examples of highly reliable Markovian systems. We compare it to a previously proposed heuristic that combines forcing with balanced failure biaising. We also exhibit the exact zero-variance change of measure for these examples and compare it with these two approximations.