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

Dror Givon; Ioannis G. Kevrekidis; Raz Kupferman

doi:10.4310/CMS.2006.v4.n4.a2

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

Dror Givon, Ioannis G. Kevrekidis, Raz Kupferman

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

60 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 language	English
Pages (from-to)	707-729
Number of pages	23
Journal	Communications in Mathematical Sciences
Volume	4
Issue number	4
DOIs	https://doi.org/10.4310/CMS.2006.v4.n4.a2
State	Published - 2006

Bibliographical note

Publisher Copyright:
© 2006 International Press

Keywords

Dimension reduction
Projective integration
Scale separation
Singular perturbations
Stochastic differential equations

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10.4310/CMS.2006.v4.n4.a2

Cite this

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

Abstract

Bibliographical note

Keywords

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