Analysis of an importance sampling estimator for tandem queues
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Large deviations and importance sampling for a tandem network with slow-down
Queueing Systems: Theory and Applications
Fluid heuristics, Lyapunov bounds and efficient importance sampling for a heavy-tailed G/G/1 queue
Queueing Systems: Theory and Applications
Subsolutions of an Isaacs Equation and Efficient Schemes for Importance Sampling
Mathematics of Operations Research
Importance sampling for Jackson networks
Queueing Systems: Theory and Applications
On large deviations theory and asymptotically efficient Monte Carlo estimation
IEEE Transactions on Information Theory
On the inefficiency of state-independent importance sampling in the presence of heavy tails
Operations Research Letters
Rare events in cancer recurrence timing
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)
Hi-index | 0.00 |
In this article we explain some connections between Lyapunov methods and subsolutions of an associated Isaacs equation for the design of efficient importance sampling schemes. As we shall see, subsolutions can be derived by taking an appropriate limit of an associated Lyapunov inequality. They have been recently proposed in several works of Dupuis, Wang, and others and applied to address several important problems in rare-event simulation. Lyapunov inequalities have been used for testing the efficiency of state-dependent importance sampling schemes in heavy-tailed or discrete settings in a variety of works by Blanchet, Glynn, and others. While subsolutions provide an analytic criterion for the construction of efficient samplers, Lyapunov inequalities are useful for finding more precise information, in the form of bounds, for the behavior of the coefficient of variation of the associated importance sampling estimator in the prelimit. In addition, Lyapunov inequalities provide insight into the various mollification procedures that are often required in constructing associated subsolutions. Our aim is to demonstrate that applying Lyapunov inequalities for verification of efficiency can help both guide the selection of various mollification parameters and sharpen the information on the efficiency gain induced by the sampler.