Rare-Event Simulation for Stochastic Recurrence Equations with Heavy-Tailed Innovations

Jose Blanchet, Henrik Hult, Kevin Leder

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this article, rare-event simulation for stochastic recurrence equations of the form [formula ommitted] is studied, where {An; n ≥ 1} and {Bn; 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 B1 is regularly varying, whereas the distribution of A1 has a suitably light tail. The problem of efficient estimation, via simulation, of quantities such as P{Xn> b} and P{supk=nXk> 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.

Original languageEnglish (US)
Pages (from-to)1-25
Number of pages25
JournalACM Transactions on Modeling and Computer Simulation
Volume23
Issue number4
DOIs
StatePublished - Oct 1 2013

Keywords

  • Algorithms
  • Importance sampling
  • Performance
  • Theory
  • heavy-tails
  • stochastic recurrence equations

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