An iterative stochastic method for simulating large deviations and rare events

Graham M. Donovan*, William L. Kath

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We describe an iterative method capable of determining large deviations responsible for rare events of interest in lightwave systems with additive noise. The method makes use of the singular value decomposition (SVD) to efficiently compute the most important directions in state space, and a stochastic optimization scheme known as the cross-entropy (CE) method to determine the most probable manner in which these large deviations arise. Information from the SVD and CE steps of the method provides a basis for performing importance sampling with Monte Carlo simulation, allowing one to determine the probabilities of the rare events associated with such large deviations. We apply the combined method to investigate some of the mechanisms affecting large amplitude fluctuations in optical systems.

Original languageEnglish (US)
Pages (from-to)903-924
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume71
Issue number3
DOIs
StatePublished - 2011

Keywords

  • Cross-entropy method
  • Gaussian white noise
  • Importance sampling
  • Monte Carlo simulation
  • Singular value decomposition
  • Variance reduction

ASJC Scopus subject areas

  • Applied Mathematics

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