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Rare-Event Simulation for Stochastic Recurrence Equations with Heavy-Tailed Innovations
Columbia University.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0001-9210-121X
University of Minnesota.
2013 (English)In: ACM Transactions on Modeling and Computer Simulation, ISSN 1049-3301, Vol. 23, no 4, 22- p.Article in journal (Refereed) Published
Abstract [en]

In this article, rare-event simulation for stochastic recurrence equations of the form Xn+1 = A(n+1)X(n) + Bn+1, X-0 = 0 is studied, where {A(n);n >= 1} and {B-n;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 B-1 is regularly varying, whereas the distribution of A(1) has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as P{X-n > b} and P{sup(k <= n) X-k > 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.

Place, publisher, year, edition, pages
2013. Vol. 23, no 4, 22- p.
Keyword [en]
Importance sampling, stochastic recurrence equations, heavy-tails
National Category
Probability Theory and Statistics
URN: urn:nbn:se:kth:diva-136970DOI: 10.1145/2517451ISI: 000329124400002OAI: diva2:677611

QC 20140123. Updated from accepted to published.

Research supported by the Göran Gustafsson Foundation. 

Available from: 2013-12-10 Created: 2013-12-10 Last updated: 2014-01-23Bibliographically approved

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