Proceedings of the 33nd conference on Winter simulation
Simulating heavy tailed processes using delayed hazard rate twisting
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance sampling for sums of random variables with regularly varying tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Importance Sampling for Weighted-Serve-the-Longest-Queue
Mathematics of Operations Research
Asymptotic robustness of estimators in rare-event simulation
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On importance sampling with mixtures for random walks with heavy tails
ACM Transactions on Modeling and Computer Simulation (TOMACS)
On Lyapunov Inequalities and Subsolutions for Efficient Importance Sampling
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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In this article, rare-event simulation for stochastic recurrence equations of the form Xn+1=An+1Xn+Bn+1, X0=0 is studied, where {An;n≥ 1} and {Bn;n≥ 1} are independent sequences consisting of independent and identically distributed real-valued random variables. It is assumed that the tail of the distribution of B1 is regularly varying, whereas the distribution of A1 has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as P{Xnb} and P{supk≤nXk b} for large b and n is studied. Importance sampling strategies are investigated that provide unbiased estimators with bounded relative error as b and n tend to infinity.