Importance sampling for Jackson networks
Queueing Systems: Theory and Applications
Importance Sampling for Weighted-Serve-the-Longest-Queue
Mathematics of Operations Research
On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling
ACM Transactions on Modeling and Computer Simulation (TOMACS)
An Iterative Procedure for Constructing Subsolutions of Discrete-Time Optimal Control Problems
SIAM Journal on Control and Optimization
Rare events in cancer recurrence timing
Proceedings of the Winter Simulation Conference
Efficient importance sampling under partial information
Proceedings of the Winter Simulation Conference
Rare event simulation techniques
Proceedings of the Winter Simulation Conference
Rare event simulation for rough energy landscapes
Proceedings of the Winter Simulation Conference
Importance sampling for stochastic recurrence equations with heavy tailed increments
Proceedings of the Winter Simulation Conference
Efficient importance sampling schemes for a feed-forward network
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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It was established in Dupuis and Wang [Dupuis, P., H. Wang. 2004. Importance sampling, large deviations, and differential games. Stoch. Stoch. Rep.76 481--508, Dupuis, P., H. Wang. 2005. Dynamic importance sampling for uniformly recurrent Markov chains. Ann. Appl. Probab.15 1--38] that importance sampling algorithms for estimating rare-event probabilities are intimately connected with two-person zero-sum differential games and the associated Isaacs equation. This game interpretation shows that dynamic or state-dependent schemes are needed in order to attain asymptotic optimality in a general setting. The purpose of the present paper is to show that classical subsolutions of the Isaacs equation can be used as a basic and flexible tool for the construction and analysis of efficient dynamic importance sampling schemes. There are two main contributions. The first is a basic theoretical result characterizing the asymptotic performance of importance sampling estimators based on subsolutions. The second is an explicit method for constructing classical subsolutions as a mollification of piecewise affine functions. Numerical examples are included for illustration and to demonstrate that simple, nearly asymptotically optimal importance sampling schemes can be obtained for a variety of problems via the subsolution approach.