TY - GEN

T1 - Importance sampling for stochastic recurrence equations with heavy tailed increments

AU - Blanchet, Jose

AU - Hult, Henrik

AU - Leder, Kevin

PY - 2011

Y1 - 2011

N2 - 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 X n+1 = A n+1X n+B n+1, X 0 = 0, 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.

AB - 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 X n+1 = A n+1X n+B n+1, X 0 = 0, 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.

UR - http://www.scopus.com/inward/record.url?scp=84858031220&partnerID=8YFLogxK

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U2 - 10.1109/WSC.2011.6148074

DO - 10.1109/WSC.2011.6148074

M3 - Conference contribution

AN - SCOPUS:84858031220

SN - 9781457721083

T3 - Proceedings - Winter Simulation Conference

SP - 3824

EP - 3831

BT - Proceedings of the 2011 Winter Simulation Conference, WSC 2011

T2 - 2011 Winter Simulation Conference, WSC 2011

Y2 - 11 December 2011 through 14 December 2011

ER -