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Importance sampling for stochastic recurrence equations with heavy-tailed increments
Columbia University.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9210-121X
University of Minnesota.
2011 (English)In: Proceedings of the 2011 Winter Simulation Conference, 2011, 3824-3831 p.Conference paper (Other academic)
Abstract [en]

Importance sampling in the setting of heavy tailed random variables has generally focused on models withadditive noise terms. In this work we extend this concept by considering importance sampling for theestimation of rare events in Markov chains of the formXn+1 = An+1Xn+Bn+1; X0 = 0;where the Bn’s and An’s are independent sequences of independent and identically distributed (i.i.d.) randomvariables and the Bn’s are regularly varying and the An’s are suitably light tailed relative to Bn. We focuson efficient estimation of the rare event probability P(Xn > b) as b%¥. In particular we present a stronglyefficient importance sampling algorithm for estimating these probabilities, and present a numerical exampleshowcasing the strong efficiency.

Place, publisher, year, edition, pages
2011. 3824-3831 p.
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-84217DOI: 10.1109/WSC.2011.6148074ScopusID: 2-s2.0-84858031220OAI: diva2:499190
2011 Winter Simulation Conference. Phoenix, US. 11-14 Dec. 2011
QC 20120410Available from: 2012-02-13 Created: 2012-02-13 Last updated: 2012-04-10Bibliographically approved

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