Title :
Importance sampling for stochastic recurrence equations with heavy tailed increments
Author :
Blanchet, Jose ; Hult, Henrik ; Leder, Kevin
Author_Institution :
Columbia Univ., New York, NY, USA
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 Bn´s and An´s are independent sequences of independent and identically distributed (i.i.d.) random variables and the Bn´s are regularly varying and the An´s are suitably light tailed relative to Bn. We focus on efficient estimation of the rare event probability P(Xn >; 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.
Keywords :
estimation theory; importance sampling; probability; random processes; random sequences; Markov chain; additive noise terms; distributed random variables; heavy tailed increment; importance sampling algorithm; independent random variables; rare event estimation; rare event probability; stochastic recurrence equation; Equations; Estimation; Lyapunov methods; Markov processes; Mathematical model; Monte Carlo methods; Random variables;
Conference_Titel :
Simulation Conference (WSC), Proceedings of the 2011 Winter
Conference_Location :
Phoenix, AZ
Print_ISBN :
978-1-4577-2108-3
Electronic_ISBN :
0891-7736
DOI :
10.1109/WSC.2011.6148074