STRONG CONVERGENCE OF PROJECTIVE INTEGRATION SCHEMES FOR SINGULARLY PERTURBED STOCHASTIC DIFFERENTIAL SYSTEMS

Dror Givon, Ioannis G. Kevrekidis, Raz Kupferman

Research output: Contribution to journalArticlepeer-review

59 Scopus citations

Abstract

We study the convergence of the slow (or "essential") components of singularly perturbed stochastic differential systems to solutions of lower dimensional stochastic systems (the "effective", or "coarse" dynamics). We prove strong, mean-square convergence in systems where both fast and slow components are driven by noise, with full coupling between fast and slow components. We analyze a class of "projective integration" methods, which consist of a hybridization between a standard solver for the slow components, and short runs for the fast dynamics, which are used to estimate the effect that the fast components have on the slow ones.

Original languageAmerican English
Pages (from-to)707-729
Number of pages23
JournalCommunications in Mathematical Sciences
Volume4
Issue number4
DOIs
StatePublished - 2006

Bibliographical note

Publisher Copyright:
© 2006 International Press

Keywords

  • Dimension reduction
  • Projective integration
  • Scale separation
  • Singular perturbations
  • Stochastic differential equations

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