J. Blanchet, H. Hult and K. Leder, “Importance sampling for stochastic recurrence equations with heavy tailed increments,” Proceedings of the 2011 Winter Simulation Conference (WSC), Phoenix, AZ, USA, 2011, pp. 3824-3831, doi: 10.1109/WSC.2011.6148074.
Abstract
Importance sampling in the setting of heavy tailed random variables has generally focused on models with additive noise terms. In this work we extend this concept by considering importance sampling for the estimation of rare events in Markov chains of the form equation where the B n 's and A n 's are independent sequences of independent and identically distributed (i.i.d.) random variables and the B n 's are regularly varying and the A n 's are suitably light tailed relative to B n . We focus on efficient estimation of the rare event probability P(X n >; b) as b↗∞. In particular we present a strongly efficient importance sampling algorithm for estimating these probabilities, and present a numerical example showcasing the strong efficiency.
Authors
Jose Blanchet, Henrik Hult, Kevin Leder
Publication date
2011/12/11
Conference
Proceedings of the 2011 Winter Simulation Conference (WSC)
Pages
3824-3831
Publisher
IEEE
